AI & ChatGPT searches , social queries for STRICT INITIAL-OBJECT
Search references for STRICT INITIAL-OBJECT. Phrases containing STRICT INITIAL-OBJECT
See searches and references containing STRICT INITIAL-OBJECT!
Search references for STRICT INITIAL-OBJECT. Phrases containing STRICT INITIAL-OBJECT
See searches and references containing STRICT INITIAL-OBJECT!STRICT INITIAL-OBJECT
Special objects used in (mathematical) category theory
one with a zero object. A strict initial object I is one for which every morphism into I is an isomorphism (strict terminal objects are defined analogously)
Initial_and_terminal_objects
Object in category theory
In the mathematical discipline of category theory, a strict initial object is an initial object 0 of a category C with the property that every morphism
Strict_initial_object
Mathematical set containing no elements
space is the unique initial object in the category of topological spaces with continuous maps. In fact, it is a strict initial object: only the empty set
Empty_set
Category admitting tensor products
coproducts is monoidal with the coproduct as the monoidal product and the initial object as the unit. Such a monoidal category is called cocartesian monoidal
Monoidal_category
Concurrency control method
serializability. A transaction is holding a lock on an object if that transaction has acquired a lock on that object which has not yet been released. For 2PL, the
Two-phase_locking
Generalization of category theory
concept is too strict for some purposes in for example, homotopy theory, where "weak" structures arise in the form of higher categories, strict cubical higher
Higher_category_theory
Class of mathematical orderings
a non-strict well ordering, then < is a strict well ordering. A relation is a strict well ordering if and only if it is a well-founded strict total order
Well-order
Characterizing property of mathematical constructions
Universal morphisms can also be thought more abstractly as initial or terminal objects of a comma category (see § Connection with comma categories,
Universal_property
In mathematics, invertible homomorphism
examples, the "equal" objects contain elements that are not set-theoretically identical, so they are not equal in this strict sense. However, because
Isomorphism
injective object. 2. The term “projective limit” is another name for an inverse limit. PROP A PROP is a symmetric strict monoidal category whose objects are
Glossary_of_category_theory
Relationship between two functors abstracting many common constructions
isomorphism Φ : homC(F−,−) → homD(−,G−). For each object X in C, each object Y in D, as (F(Y), ηY) is an initial morphism, then ΦY, X is a bijection, where ΦY
Adjoint_functors
Proposed parameter in linguistics
and non-rigid) and head-initial types. The identification of headedness is based on the following: the order of subject, object, and verb the relationship
Head-directionality_parameter
General theory of mathematical structures
category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the source and the target of
Category_theory
Object whose state cannot be modified after it is created
In object-oriented (OO) and functional programming, an immutable object (unchangeable object) is an object whose state cannot be modified after it is
Immutable_object
Mathematical set with an ordering
also called strict partial orders. Strict and non-strict partial orders can be put into a one-to-one correspondence, so for every strict partial order
Partially_ordered_set
Order whose elements are all comparable
ISSN 0031-952X. JSTOR 24340068. This definition resembles that of an initial object of a category, but is weaker. Roland Fraïssé (December 2000). Theory
Total_order
Mathematical object that generalizes the standard notions of sets and functions
the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category
Category_(mathematics)
focuses on strict 2-groups. A strict 2-group is a strict monoidal category in which every morphism is invertible and every object has a strict inverse (so
2-group
Order of execution of transactions in transaction processing
satisfied: If the transaction T i {\displaystyle T_{i}} in S1 reads an initial value for object X, so does the same transaction T i {\displaystyle T_{i}} in S2
Database_transaction_schedule
Generalization of category
2-morphism is a natural transformation between functors. The concept of a strict 2-category was first introduced by Charles Ehresmann in his work on enriched
2-category
Central object of study in category theory
\eta _{X}:F(X)\to G(X)} is natural in X {\displaystyle X} . If, for every object X {\displaystyle X} in C {\displaystyle {\mathcal {C}}} , the morphism η
Natural_transformation
Mathematical concept
also referred to as universal co-cones. They can be characterized as initial objects in the category of co-cones from F {\displaystyle F} . As with limits
Limit_(category_theory)
Linguistic classification
In syntax, verb-initial (V1) word order is a word order in which the verb appears before the subject and the object. In the more narrow sense, this term
Verb-initial_word_order
Mapping between categories
where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to
Functor
Category theory constructs
( a ) {\displaystyle \delta _{F}(a)=\delta (Fa):MF(a)\to RF(a)} for any object a {\displaystyle a} of A . {\displaystyle \mathbf {A} .} The functor R is
Kan_extension
Map (arrow) between two objects of a category
composition when it is defined, and existence of an identity morphism for every object), and the outcome of the composition is a morphism. Morphisms and categories
Morphism
Categorical generalization of a function space in set theory
object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects
Exponential_object
Embedding of categories into functor categories
fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only
Yoneda_lemma
Construction in category theory
"glue together" several related objects, the precise gluing process being specified by morphisms between the objects. Inverse limits can be defined in
Inverse_limit
Abstract mathematics relationship
object c of C is an initial object (or terminal object, or zero object), if and only if Fc is an initial object (or terminal object, or zero object)
Equivalence_of_categories
Most general completion of a commutative square given two morphisms with same codomain
the morphisms f {\displaystyle f} and g {\displaystyle g} consists of an object P {\displaystyle P} and two morphisms p 1 : P → X {\displaystyle p_{1}:P\rightarrow
Pullback_(category_theory)
Generalized object in category theory
In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas
Product_(category_theory)
Most general completion of a commutative square given two morphisms with same domain
and coequalizers (if there is an initial object) in the sense that: Coproducts are a pushout from the initial object, and the coequalizer of f, g : X
Pushout_(category_theory)
Mathematical category
of X {\displaystyle X} and Y {\displaystyle Y} over their sum is the initial object in C {\displaystyle C} . All equivalence relations in C {\displaystyle
Topos
Object in category theory
numbers object (NNO) is an object endowed with a recursive structure similar to natural numbers. More precisely, in a category E with a terminal object 1,
Natural_numbers_object
Category-theoretic construction
vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is
Coproduct
Markup language which places HTML in XML form
1.0 Strict document.<br /> <img id="validation-icon" src="http://www.w3.org/Icons/valid-xhtml10" alt="Valid XHTML 1.0 Strict"/><br /> <object id="pdf-object"
XHTML
Special case of colimit in category theory
construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector
Direct_limit
WWII Soviet heavy tank
on the basis of the Object 220, in the form of the Object 221 (with an 85 mm gun), Object 222 (with the F-32 76.2 mm gun) and Object 223 (built to develop
KV_tank_family
Type of category in category theory
x^{y+z}=x^{y}\times x^{z}} the initial object is the coproduct identity: 0 + x = x {\displaystyle 0+x=x} the initial object is the product zero: x × 0 =
Cartesian_closed_category
terminal object 1, binary coproducts (denoted by +), and binary products (denoted by ×), a list object over A can be defined as the initial algebra of
List_object
Basic word order type
In linguistic typology, a verb–object–subject or verb–object–agent language, commonly abbreviated VOS or VOA, is one in which most sentences arrange their
Verb–object–subject word order
Verb–object–subject_word_order
Quotient space of a codomain of a linear map by the map's image
of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain). Intuitively, given an equation
Cokernel
Injective homomorphism
left-cancellative morphism. That is, an arrow f : X → Y such that for all objects Z and all morphisms g1, g2: Z → X, f ∘ g 1 = f ∘ g 2 ⟹ g 1 = g 2 . {\displaystyle
Monomorphism
Category with direct sums and certain types of kernels and cokernels
mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable
Abelian_category
A category C consists of objects and morphisms between these objects. The morphisms reflect relations between the objects. In many situations, it is
Localization_of_a_category
Markup language for documents
building blocks of HTML pages. With HTML constructs, images and other objects such as interactive forms may be embedded into the rendered page. HTML
HTML
Certain generalizations of groups
The strict 2-group is the group object in the category of small categories. Given a category C with finite coproducts, a cogroup object is an object G of
Group_object
Theorem in category theory
} and given an object B {\displaystyle B} in it, if there is a weakly point-surjective morphism f {\displaystyle f} from some object A {\displaystyle
Lawvere's_fixed-point_theorem
Applications of category theory
Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels
Applied_category_theory
Programming language and superset of JavaScript
libraries, much like C++ header files can describe the structure of existing object files. This enables other programs to use the values defined in the files
TypeScript
Category whose objects and morphisms are inside a bigger category
strictly full. A subcategory of C {\displaystyle {\mathcal {C}}} is wide or lluf (a term first posed by Peter Freyd) if it contains all the objects of
Subcategory
Type of category in category theory
it). The empty product, is a final object and the empty product in the case of an empty diagram, an initial object. Both being limits, they are not finite
Additive_category
Category in which all small limits exist
not products, coproducts, equalizers, coequalizers, terminal objects, or initial objects. Abstract and Concrete Categories, Jiří Adámek, Horst Herrlich
Complete_category
Mathematical category whose hom sets form Abelian groups
terminal (a nullary product) and initial (a nullary coproduct), it will in fact be a zero object. Indeed, the term "zero object" originated in the study of
Preadditive_category
Concept in mathematics
Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels
Tensor–hom_adjunction
Mathematical concept
\mathbf {C} \to \mathbf {X} } is a universal dinatural transformation from an object e {\displaystyle e} of X {\displaystyle \mathbf {X} } to S {\displaystyle
End_(category_theory)
Software component technology from Microsoft
Component Object Model (COM) is a binary-interface technology for software components from Microsoft that enables using objects in a language-neutral
Component_Object_Model
Category of non-empty finite ordinals and order-preserving maps
finite ordinals as objects, thought of as totally ordered sets, and (non-strictly) order-preserving functions as morphisms. The objects are commonly denoted
Simplex_category
Concept in mathematical category theory
{\displaystyle A\otimes B} is, in a certain strict sense, naturally isomorphic to B ⊗ A {\displaystyle B\otimes A} for all objects A {\displaystyle A} and B {\displaystyle
Symmetric_monoidal_category
Aspect of category theory
objects X and Y and two parallel morphisms f, g : X → Y. More explicitly, a coequalizer of the parallel morphisms f and g can be defined as an object
Coequalizer
Relation of categories in category theory
C is a category with an initial object s, then the slice category (s↓C) is isomorphic to C. Dually, if t is a terminal object in C, the functor category
Isomorphism_of_categories
Category theory concept
(X,\operatorname {id} )} is a terminal object of C / X {\displaystyle {\mathcal {C}}/X} and an initial object of X / C {\displaystyle X/{\mathcal {C}}}
Overcategory
Category whose hom sets have algebraic structure
hom-set) associated with every pair of objects is replaced by an object in some fixed monoidal category of "hom-objects". In order to emulate the (associative)
Enriched_category
Abstract homotopical model for topological spaces
for topological spaces. One model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure)
∞-groupoid
Generalization of a category
ordinary categories, they contain objects (the 0-simplices of the simplicial set) and morphisms between these objects (1-simplices). But unlike categories
Quasi-category
Concept in category theory
commutativity, but keeps all the operations. Occasionally the object may include extra sets not defined strictly in terms of the underlying set (in this case, which
Forgetful_functor
Functor type
universal morphism from the one-point set {•} to the functor F or as an initial object in the category of elements of F. The natural transformation induced
Representable_functor
Set whose elements all belong to another set
A is a proper (or strict) subset of B, denoted by A ⊊ B {\displaystyle A\subsetneq B} , or equivalently, B is a proper (or strict) superset of A, denoted
Subset
Object that represents a simple entity whose equality is not based on identity
"VALJO" (VALue Java Object) has been coined to refer to the stricter set of rules necessary for a correctly defined immutable value object. public class StreetAddress
Value_object
Surjective homomorphism
morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g1, g2: Y → Z, g 1 ∘ f = g 2 ∘ f ⟹ g 1 = g 2 . {\displaystyle
Epimorphism
Theoretical paradox resulting from time travel
ontological paradox, occurs when any event, such as an action, information, an object, or a person, ultimately causes itself, as a consequence of either retrocausality
Temporal_paradox
Set of arguments where two or more functions have the same value
consists of an object E and a morphism eq : E → X satisfying f ∘ e q = g ∘ e q {\displaystyle f\circ eq=g\circ eq} , and such that, given any object O and morphism
Equaliser_(mathematics)
Small Solar System body with an orbit that can bring it close to Earth
Atens: 2,952 (7.90%) Comets: 123 (0.33%) Atiras: 34 (0.09%) A near-Earth object (NEO) is by definition any small Solar System body orbiting the Sun whose
Near-Earth_object
Family of higher-order functions
reason, such languages often provide a stricter variant of left folding which forces the evaluation of the initial parameter before making the recursive
Fold_(higher-order_function)
Construction in category theory
a universal cone from F is a universal morphism from F to Δ, or an initial object in (F ↓ Δ). The limit of F is a universal cone to F, and the colimit
Cone_(category_theory)
Collection of maps which give the same result
commutes (the notion of diagram strictly generalizes commutative diagram). As a simple example, the diagram of a single object with an endomorphism ( f : X
Commutative_diagram
Concept in software engineering
often seen in terms of services, but objects could be an equally powerful approach. The DSP's initial 'Naked Object Architecture' was developed by an external
Naked_objects
Category theory
{\displaystyle C} as above, we associate with each object X {\displaystyle X} in C {\displaystyle C} a new object X T {\displaystyle X_{T}} , and for each morphism
Kleisli_category
Variant of the notion of the center of a monoid, group, or ring to a category
{\mathcal {Z(C)}}} , is the category whose objects are pairs ( A , u ) {\displaystyle (A,u)} consisting of an object A {\displaystyle A} of C {\displaystyle
Center_(category_theory)
Overview of and topical guide to category theory
Category of magmas Initial object Terminal object Zero object Subobject Group object Magma object Natural number object Exponential object Epimorphism Monomorphism
Outline_of_category_theory
Rate of change of velocity
physics, acceleration is a measure of how fast and in what direction an object's speed and direction of motion are changing. It is defined as the rate of
Acceleration
Mathematical category with weak equivalences, fibrations and cofibrations
closed model category has a terminal object by completeness and an initial object by cocompleteness, since these objects are the limit and colimit, respectively
Model_category
Motion of a body subject only to gravity
falling object may not necessarily be falling down in the vertical direction. If the common definition of the word "fall" is used, an object moving upwards
Free_fall
Library of modules (software)
The Perl Object Environment (POE) is a library of Perl modules written in the Perl programming language by Rocco Caputo et al. From CPAN: "POE originally
Perl_Object_Environment
Functors which are surjective and injective on hom-sets
faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full
Full_and_faithful_functors
Mathematical construction used in homotopy theory
category. The objects of Δ are nonempty totally ordered finite sets, and the morphisms (non-strictly) order-preserving functions. Each object is uniquely
Simplicial_set
Correspondence between properties of a category and its opposite
two-sorted first order language with objects and morphisms as distinct sorts, together with the relations of an object being the source or target of a morphism
Dual_(category_theory)
High-level programming language
conforms to the ECMAScript standard. It has dynamic typing, prototype-based object-orientation, and first-class functions. It is multi-paradigm, supporting
JavaScript
Higher categorical generalization of a topos
an ∞-topos (infinity-topos) is, roughly, an ∞-category such that its objects behave like sheaves of spaces with some choice of Grothendieck topology;
∞-topos
Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels
Lift_(mathematics)
Hypothesis in mathematical category theory
ISSN 1245-530X. Hadzihasanovic 2020 Simpson, Carlos (1998). "Homotopy types of strict 3-groupoids". arXiv:math/9810059. Land 2021, 2.1 Joyal’s Special Horn Lifting
Homotopy_hypothesis
Type of quotient object in mathematics
another category by identifying sets of morphisms. Formally, it is a quotient object in the category of (locally small) categories, analogous to a quotient group
Quotient_category
Human-readable data serialization language
format. YAML makes minimal use of indicator characters compared to TOML's strict requirement of quotation marks and square brackets. YAML's use of significant
YAML
Soviet main battle tank
coming back from Nizhniy Tagil, with Morozov at its head. A project named object 430 led to three prototypes which were tested in Kubinka in 1958. Those
T-64
Philosophical study of beauty and art
appreciation. Aesthetic properties are features that influence the appeal of objects. They include aesthetic values, which express positive or negative qualities
Aesthetics
Software optimization technique
which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which avoids repeated evaluations (by the use of sharing)
Lazy_evaluation
General-purpose programming language
was originally a thin layer on top of C, and remains a strict superset of C that permits object-oriented programming using a hybrid dynamic/static typing
C_(programming_language)
Indexed collection of objects and morphisms in a category
diagram is then an object in this category. Given any object A in C, one has the constant diagram, which is the diagram that maps all objects in J to A, and
Diagram_(category_theory)
Functor that preserves short exact sequences
calculations because they can be directly applied to presentations of objects. Much of the work in homological algebra is designed to cope with functors
Exact_functor
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
Girl/Female
Tamil
The initial reality
Surname or Lastname
English (Cornwall)
English (Cornwall) : perhaps, as Reaney suggests, a variant of Strutt.
Surname or Lastname
English
English : nickname from Middle English streit ‘narrow’, ‘strict’ (Anglo-Norman French estreit).German and Jewish (Ashkenazic) : nickname for a quarrelsome person, from Middle High German strīt, German Streit ‘strife’, ‘argument’.
Boy/Male
Hindu, Indian
Morally Strict; Simple
Surname or Lastname
English
English : habitational name from any of the various places, for example in Hertfordshire, Kent, and Somerset, so named from Old English strǣt ‘paved highway’, ‘Roman road’ (Latin strata (via)). In the Middle Ages the word at first denoted a Roman road but later also came to denote the main street in a town or village, and so the surname may also have been a topographic name for someone who lived on a main street.Jewish : Americanized form of the Sephardic surname Chetrit, of uncertain origin.Americanized form of Ashkenazic Jewish Strasser and a number of other similar surnames.The Rev. Nicholas Street (1603–74) came from England to Taunton, MA, between 1630 and 1638, and later moved to New Haven, CT, where his descendant Augustus Russell Street, a leader in art education, was born in 1791 and went on to become one of the most important early benefactors of Yale College.
Surname or Lastname
English
English : metonymic occupational name from Middle English strike, the stick used by a Striker.
Boy/Male
American, British, English
Severe; Strict
Boy/Male
Spanish
Strict; restrained.
Female
Hebrew
(שָׂרַית) Diminutive form of Hebrew Sarah, SARIT means "noble lady, princess."
Surname or Lastname
English
English : from Middle English stride ‘(long) pace’ (from stride(n) ‘to walk with long steps’), presumably a nickname for someone with long legs or whose gait had a purposeful air, although Reaney and Wilson suggest it may also have been a topographic name for someone who lived by a crossing point over a stream, presumably no wider than a stride. They cite as an example a place known as The Strid, in North Yorkshire.
Boy/Male
Hindu, Indian
The Sprout; Initial
Boy/Male
Afghan, Australian
Strict
Female
French
French form of Latin Viatrix, BÉATRICE means "voyager (through life)."
Surname or Lastname
English
English : of uncertain origin, probably from the Old Norse byname Strútr (from a vocabulary word referring to a cone-like ornament on a headdress or cap). Alternatively it may be a nickname for an argumentative person, from Middle English strut(t) ‘quarrel’.German : topographic name from Middle High German struot, strūt ‘brush’, ‘thicket’, ‘swamp’, or a habitational name from any of several places named Struth with this word.
Surname or Lastname
English
English : topographic name for someone who lived on or by a strip of land, Old English strīp.
Boy/Male
English
Strict. Restrained. Surname.
Surname or Lastname
English
English : variant spelling of Street.
Boy/Male
Arabic, Muslim
Lion; Difficult; Strict
Boy/Male
English
Strict. Restrained. Surname.
Girl/Female
Indian
The initial reality
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
Male
English
Anglicized form of Greek Henoch (Hebrew Chanowk), ENOCH means "dedicated" or "initiated." In the bible, this is the name of the eldest son of Cain, and a son of Jared the father of Methuselah.
Girl/Female
Muslim
Freshness of splendor
Girl/Female
Indian, Parsi
Clear Water
Girl/Female
Arabic, Assamese, British, English, French, Greek, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Slavic, Tamil, Telugu
Feminine of Michael; Like the Lord; Variant of Melissa; Bee; Lord Krishna's Devotee; Smile; Teddy Bear in Russian
Male
French
French form of Latin Franciscus, FRANC means "French."
Girl/Female
Gujarati, Hindu, Indian
Dedication; A Pledge; A Lamp; Light; Radiant; Goddess Lakshmi
Female
English
Pet form of English Maud, MAUDIE means "mighty in battle."
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
Little Plant; Small Plant
Male
African
God is the king.
Boy/Male
Hindu, Indian, Marathi
Divine Diamond
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
STRICT INITIAL-OBJECT
n.
Strife; contention.
a.
Placed at the beginning; standing at the head, as of a list or series; as, the initial letters of a name.
a.
Strained; drawn close; tight; as, a strict embrace; a strict ligature.
n.
Ostrich.
a.
Rigidly; interpreted; exactly limited; confined; restricted; as, to understand words in a strict sense.
a.
Governed or governing by exact rules; observing exact rules; severe; rigorous; as, very strict in observing the Sabbath.
p. pr. & vb. n.
of Initial
a.
Of or pertaining to the beginning; marking the commencement; incipient; commencing; as, the initial symptoms of a disease.
v. t.
To deprive of strings; to strip the strings from; as, to string beans. See String, n., 9.
imp. & p. p.
of Initial
adv.
In a strict manner; closely; precisely.
superl.
Strict; scrupulous; rigorous.
v. t.
To put an initial to; to mark with an initial of initials.
a.
Exact; accurate; precise; rigorously nice; as, to keep strict watch; to pay strict attention.
a.
Tense; not relaxed; as, a strict fiber.
v. t.
To restrict the tenure of; as, to astrict lands. See Astriction, 4.
n.
See Astrict, and Astriction.
v. t.
To come in collision with; to strike against; as, a bullet struck him; the wave struck the boat amidships; the ship struck a reef.
adv.
In an initial or incipient manner or degree; at the beginning.
a.
Close; narrow; strict.