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OVERCATEGORY

  • Overcategory

    • Category theory concept

    In mathematics, an overcategory (also called a slice category) is a construction from category theory used in multiple contexts, such as with covering

    Overcategory

    Overcategory

  • Category (mathematics)

    • Mathematical object that generalizes the standard notions of sets and functions

    object X {\displaystyle X} of C {\displaystyle {\mathcal {C}}} , the overcategory or slice category C / X {\displaystyle {\mathcal {C}}/X} consists of

    Category (mathematics)

    Category (mathematics)

    Category_(mathematics)

  • Isomorphism

    • In mathematics, invertible homomorphism

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Isomorphism

    Isomorphism

    Isomorphism

  • Category theory

    • General theory of mathematical structures

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Category theory

    Category theory

    Category_theory

  • Morphism

    • Map (arrow) between two objects of a category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Morphism

    Morphism

  • Full and faithful functors

    • Functors which are surjective and injective on hom-sets

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Full and faithful functors

    Full_and_faithful_functors

  • Yoneda lemma

    • Embedding of categories into functor categories

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Yoneda lemma

    Yoneda_lemma

  • Kan extension

    • Category theory constructs

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Kan extension

    Kan_extension

  • Coproduct

    • Category-theoretic construction

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Coproduct

    Coproduct

  • Topos

    • Mathematical category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Topos

    Topos

  • Functor

    • Mapping between categories

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Functor

    Functor

  • Initial and terminal objects

    • Special objects used in (mathematical) category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Initial and terminal objects

    Initial_and_terminal_objects

  • Adjoint functors

    • Relationship between two functors abstracting many common constructions

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Adjoint functors

    Adjoint_functors

  • Diagram (category theory)

    • Indexed collection of objects and morphisms in a category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Diagram (category theory)

    Diagram_(category_theory)

  • Cone (category theory)

    • Construction in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Cone (category theory)

    Cone_(category_theory)

  • Tannakian formalism

    • Monoidal category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Tannakian formalism

    Tannakian_formalism

  • Limit (category theory)

    • Mathematical concept

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Limit (category theory)

    Limit_(category_theory)

  • Natural transformation

    • Central object of study in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Natural transformation

    Natural_transformation

  • Inverse limit

    • Construction in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Inverse limit

    Inverse_limit

  • Representable functor

    • Functor type

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Representable functor

    Representable_functor

  • Glossary of category theory

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Glossary of category theory

    Glossary_of_category_theory

  • Lawvere's fixed-point theorem

    • Theorem in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Lawvere's fixed-point theorem

    Lawvere's_fixed-point_theorem

  • Equaliser (mathematics)

    • Set of arguments where two or more functions have the same value

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Equaliser (mathematics)

    Equaliser_(mathematics)

  • Isomorphism of categories

    • Relation of categories in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Isomorphism of categories

    Isomorphism_of_categories

  • Polynomial functor

    • Endofunctor on the category V of finite-dimensional vector spaces

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Polynomial functor

    Polynomial_functor

  • Higher category theory

    • Generalization of category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Higher category theory

    Higher_category_theory

  • Cokernel

    • Quotient space of a codomain of a linear map by the map's image

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Cokernel

    Cokernel

  • Abelian category

    • Category with direct sums and certain types of kernels and cokernels

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Abelian category

    Abelian_category

  • Localization of a category

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Localization of a category

    Localization_of_a_category

  • Closed category

    • Category whose hom objects correspond (di-)naturally to objects in itself

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Closed category

    Closed_category

  • Derived functor

    • Homological construction in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Derived functor

    Derived_functor

  • Simplicial set

    • Mathematical construction used in homotopy theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Simplicial set

    Simplicial_set

  • Universal property

    • Characterizing property of mathematical constructions

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Universal property

    Universal property

    Universal_property

  • Monomorphism

    • Injective homomorphism

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Monomorphism

    Monomorphism

    Monomorphism

  • Equivalence of categories

    • Abstract mathematics relationship

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Equivalence of categories

    Equivalence_of_categories

  • Direct limit

    • Special case of colimit in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Direct limit

    Direct_limit

  • 2-ring

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    2-ring

    2-ring

  • Preadditive category

    • Mathematical category whose hom sets form Abelian groups

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Preadditive category

    Preadditive_category

  • 2-category

    • Generalization of category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    2-category

    2-category

  • Commutative diagram

    • Collection of maps which give the same result

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Commutative diagram

    Commutative diagram

    Commutative_diagram

  • Applied category theory

    • Applications of category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Applied category theory

    Applied_category_theory

  • Pullback (category theory)

    • Most general completion of a commutative square given two morphisms with same codomain

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Pullback (category theory)

    Pullback_(category_theory)

  • Comma category

    • Mathematics construct

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Comma category

    Comma_category

  • Lift (mathematics)

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Lift (mathematics)

    Lift_(mathematics)

  • Refinement (category theory)

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Refinement (category theory)

    Refinement_(category_theory)

  • Monoidal functor

    • Concept in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Monoidal functor

    Monoidal_functor

  • Tensor–hom adjunction

    • Concept in mathematics

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Tensor–hom adjunction

    Tensor–hom_adjunction

  • Sheaf (mathematics)

    • Tool to track locally defined data attached to the open sets of a topological space

    {\displaystyle \pi :E\to X} be the natural projection. Consider the overcategory Top / X {\displaystyle {\text{Top}}/X} of topological spaces over X {\displaystyle

    Sheaf (mathematics)

    Sheaf_(mathematics)

  • Cartesian closed category

    • Type of category in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Cartesian closed category

    Cartesian_closed_category

  • Product (category theory)

    • Generalized object in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Product (category theory)

    Product_(category_theory)

  • Diagonal functor

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Diagonal functor

    Diagonal_functor

  • Zero morphism

    • Bi-universal property in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Zero morphism

    Zero_morphism

  • Monoidal category

    • Category admitting tensor products

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Monoidal category

    Monoidal_category

  • Pushout (category theory)

    • Most general completion of a commutative square given two morphisms with same domain

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Pushout (category theory)

    Pushout_(category_theory)

  • Fundamental groupoid

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Fundamental groupoid

    Fundamental_groupoid

  • Fibred category

    • Concept in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Fibred category

    Fibred_category

  • Center (category theory)

    • Variant of the notion of the center of a monoid, group, or ring to a category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Center (category theory)

    Center_(category_theory)

  • Conglomerate (mathematics)

    • In mathematics, collection of classes

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Conglomerate (mathematics)

    Conglomerate_(mathematics)

  • Natural numbers object

    • Object in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Natural numbers object

    Natural numbers object

    Natural_numbers_object

  • Pre-abelian category

    • Category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Pre-abelian category

    Pre-abelian_category

  • Stable ∞-category

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Stable ∞-category

    Stable_∞-category

  • Additive category

    • Type of category in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Additive category

    Additive_category

  • Subcategory

    • Category whose objects and morphisms are inside a bigger category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Subcategory

    Subcategory

  • Simplex category

    • Category of non-empty finite ordinals and order-preserving maps

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Simplex category

    Simplex_category

  • Epimorphism

    • Surjective homomorphism

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Epimorphism

    Epimorphism

  • Functor category

    • Mathematical structures in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Functor category

    Functor_category

  • Complete category

    • Category in which all small limits exist

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Complete category

    Complete_category

  • N-group (category theory)

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    N-group (category theory)

    N-group_(category_theory)

  • Quotient category

    • Type of quotient object in mathematics

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Quotient category

    Quotient_category

  • Homotopy hypothesis

    • Hypothesis in mathematical category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Homotopy hypothesis

    Homotopy_hypothesis

  • Forgetful functor

    • Concept in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Forgetful functor

    Forgetful_functor

  • Essentially surjective functor

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Essentially surjective functor

    Essentially_surjective_functor

  • Algebraic stack

    • Generalization of algebraic spaces or schemes

    {\displaystyle {\mathcal {X}}} is a category fibered in groupoids, meaning the overcategory for some π : X → S {\displaystyle \pi :X\to S} is a groupoid The diagonal

    Algebraic stack

    Algebraic_stack

  • Product category

    • Product of two categories, in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Product category

    Product_category

  • End (category theory)

    • Mathematical concept

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    End (category theory)

    End_(category_theory)

  • Kleisli category

    • Category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Kleisli category

    Kleisli_category

  • Global element

    • Concept in category concept

    vertex, whence the global elements of a graph are its self-loops. In an overcategory C / B {\displaystyle {\mathcal {C}}/B} , the object B → id B {\displaystyle

    Global element

    Global_element

  • Free category

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Free category

    Free_category

  • 2-group

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    2-group

    2-group

  • Smooth functor

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Smooth functor

    Smooth_functor

  • Dual (category theory)

    • Correspondence between properties of a category and its opposite

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Dual (category theory)

    Dual_(category_theory)

  • Enriched category

    • Category whose hom sets have algebraic structure

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Enriched category

    Enriched_category

  • Quasi-category

    • Generalization of a category

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Quasi-category

    Quasi-category

  • Coequalizer

    • Aspect of category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Coequalizer

    Coequalizer

  • Exponential object

    • Categorical generalization of a function space in set theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Exponential object

    Exponential_object

  • Symmetric monoidal category

    • Concept in mathematical category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Symmetric monoidal category

    Symmetric_monoidal_category

  • ∞-groupoid

    • Abstract homotopical model for topological spaces

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    ∞-groupoid

    ∞-groupoid

  • Categorification

    • Connects set theory with category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Categorification

    Categorification

  • ∞-topos

    • Higher categorical generalization of a topos

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    ∞-topos

    ∞-topos

  • Outline of category theory

    • Overview of and topical guide to category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Outline of category theory

    Outline_of_category_theory

  • Dagger symmetric monoidal category

    • Symmetric monoidal category with a special involution

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Dagger symmetric monoidal category

    Dagger_symmetric_monoidal_category

  • Rig category

    • Aspect of category theory in mathematics

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Rig category

    Rig_category

  • H-object

    • ( A ∖ R ) / B {\displaystyle (A\backslash R)/B} be the associatived overcategory of objects in A ∖ R {\displaystyle A\backslash R} , then an H-object

    H-object

    H-object

  • Higher-dimensional algebra

    • Study of categorified structures

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Higher-dimensional algebra

    Higher-dimensional_algebra

  • Opposite category

    • Mathematical category formed by reversing morphisms

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Opposite category

    Opposite_category

  • String diagram

    • Graphical representation of a morphism

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    String diagram

    String_diagram

  • Exact functor

    • Functor that preserves short exact sequences

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Exact functor

    Exact_functor

  • Exalcomm

    • {\displaystyle I} is a B {\displaystyle B} -module. Then, there is an overcategory denoted Exal _ A {\displaystyle {\underline {\text{Exal}}}_{A}} (meaning

    Exalcomm

    Exalcomm

  • Point-surjective morphism

    • Concept in category theory

    (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    Point-surjective morphism

    Point-surjective_morphism

  • List object

    • (Fields) Modules (Vector spaces) Constructions on categories Comma category Overcategory Free category Functor category Kleisli category Localization of a category

    List object

    List_object

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Online names & meanings

  • Ramathaim-Zophim

    • Biblical

    Ramathaim-Zophim

    the two watch-towers

  • FRANCIS

    • Male

    English

    FRANCIS

     English name derived from Latin Franciscus, FRANCIS means "French." This name is sometimes mistakenly given to girls instead of the identically pronounced feminine form, Frances.

  • Ambady

    • Boy/Male

    Indian

    Ambady

    Lord Krishna's Childhood Place; Beautiful

  • Minni

    • Girl/Female

    Biblical

    Minni

    Reckoned, prepared.

  • MARTINA

    • Female

    English

    MARTINA

    Feminine form of Latin Martinus, MARTINA means "of/like Mars." 

  • Zin

    • Girl/Female

    Biblical, British, English

    Zin

    Buckler; Coldness

  • Henriques

    • Boy/Male

    German, Portuguese

    Henriques

    Home Ruler

  • Mohana | மோஹநா

    • Girl/Female

    Tamil

    Mohana | மோஹநா

    Attractive

  • Analeigh

    • Girl/Female

    Australian, Spanish

    Analeigh

    Grace; Favor; Similar to Anna

  • Adan

    • Girl/Female

    Irish

    Adan

    Little fire.

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OVERCATEGORY

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