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In mathematics, invertible homomorphism
an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if
Isomorphism
Topics referred to by the same term
Look up isomorphism or isomorph in Wiktionary, the free dictionary. Isomorphism or isomorph may refer to: Isomorphism, in mathematics, logic, philosophy
Isomorphism_(disambiguation)
Uniformly continuous homeomorphism
the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform
Uniform_isomorphism
graph isomorphism. Fractional isomorphism is the coarsest of several different relaxations of graph isomorphism. Whereas the graph isomorphism problem
Fractional_graph_isomorphism
Group of mathematical theorems
mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship
Isomorphism_theorems
Bijection between the vertex set of two graphs
in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs
Graph_isomorphism
Theorem in field theory
branch of mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field. The theorem
Isomorphism_extension_theorem
Unsolved problem in computational complexity theory
science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem is the computational
Graph_isomorphism_problem
Isomorphism between the tangent and cotangent bundles of a manifold
specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm
Musical_isomorphism
In mathematics, a Borel isomorphism is a measurable bijective function between two standard Borel spaces. By Souslin's theorem in standard Borel spaces
Borel_isomorphism
Similarity between organizations
institutional isomorphism and collective rationality in organizational fields. The term is borrowed from the mathematical concept of isomorphism. Isomorphism in
Isomorphism_(sociology)
The term isomorphism literally means sameness (iso) of form (morphism). In Gestalt psychology, Isomorphism is the idea that perception and the underlying
Isomorphism (Gestalt psychology)
Isomorphism_(Gestalt_psychology)
Equivalence of partially ordered sets
of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets
Order_isomorphism
Problem in theoretical computer science
that subgraph isomorphism remains NP-complete even in the planar case. Subgraph isomorphism is a generalization of the graph isomorphism problem, which
Subgraph_isomorphism_problem
Bijective group homomorphism
bijective correspondence. Thus, the definition of an isomorphism is quite natural. An isomorphism of groups may equivalently be defined as an invertible
Group_isomorphism
isomorphism entails elementary equivalence, however the converse is not generally true, but it holds for ω-saturated models. A potential isomorphism between
Potential_isomorphism
Mathematics concept
geometric version of the Satake isomorphism, proved by Ivan Mirković and Kari Vilonen (2007). Classical Satake isomorphism. Let G {\displaystyle G} be a
Satake_isomorphism
Similarity of symmetry and shape
different sizes of the atoms involved. Mitscherlich's law of isomorphism, or the law of isomorphism, is an approximate law suggesting that crystals composed
Isomorphism_(crystallography)
In algebraic geometry, the Cartier isomorphism is a certain isomorphism between the cohomology sheaves of the de Rham complex of a smooth algebraic variety
Cartier_isomorphism
Organism that does not change in shape during growth
An isomorph is an organism that does not change in shape during growth. The implication is that its volume is proportional to its cubed length, and its
Isomorph
Decision problem
isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem
Group_isomorphism_problem
Mapping which preserves all topological properties of a given space
Diffeomorphism – Isomorphism of differentiable manifolds Uniform isomorphism – Uniformly continuous homeomorphism is an isomorphism between uniform spaces
Homeomorphism
Theorem about the dual of a Hilbert space
two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural isomorphism. Let H {\displaystyle H} be a Hilbert space over a
Riesz_representation_theorem
numberings induce the same notion of computability on a set. By the Myhill isomorphism theorem, the relation of computably isomorphic coincides with the relation
Computable_isomorphism
Relation of categories in category theory
identical and differ only in the notation of their objects and morphisms. Isomorphism of categories is a strong condition and is rarely satisfied in practice
Isomorphism_of_categories
Relationship between programs and proofs
first formulation of the isomorphism was referred to (a variant of) Gentzen's sequent calculus. The observation that the isomorphism is best understood with
Curry–Howard_correspondence
Topics referred to by the same term
Isomorphism problem may refer to: graph isomorphism problem group isomorphism problem isomorphism problem of Coxeter groups This disambiguation page lists
Isomorphism_problem
Cohomology theory
Eichler–Shimura isomorphism, introduced by Eichler for complex cohomology and by Shimura (1959) for real cohomology, is an isomorphism between an Eichler
Eichler–Shimura_isomorphism
Mathematical coincidence
In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members ai and bj of two families, usually
Exceptional_isomorphism
Central object of study in category theory
\eta _{X}} is an isomorphism in D {\displaystyle {\mathcal {D}}} , then η {\displaystyle \eta } is said to be a natural isomorphism (or sometimes natural
Natural_transformation
Mathematical function, in linear algebra
way described in § Matrices (below) is a linear map, and even a linear isomorphism. The expected value of a random variable is a linear function of the
Linear_map
Uniqueness of countable dense linear orders
has only one countable model, up to isomorphism (equivalence of models). One application of Cantor's isomorphism theorem involves temporal logic, a method
Cantor's_isomorphism_theorem
Theorem relating a group with the image and kernel of a homomorphism
homomorphisms, also known as the fundamental homomorphism theorem, the first isomorphism theorem, or just the homomorphism theorem, relates the structure of two
Fundamental theorem on homomorphisms
Fundamental_theorem_on_homomorphisms
In homological algebra, a branch of mathematics, a quasi-isomorphism or quism is a morphism A → B of chain complexes (respectively, cochain complexes)
Quasi-isomorphism
Isomorphism of commutative rings constructed in the theory of Lie algebras
isomorphism, introduced by Harish-Chandra (1951), is an isomorphism of commutative rings constructed in the theory of Lie algebras. The isomorphism maps
Harish-Chandra_isomorphism
Theorem relating Milnor K-theory and Galois cohomology
the norm residue isomorphism theorem makes it possible to apply techniques applicable to the object on one side of the isomorphism to the object on the
Norm residue isomorphism theorem
Norm_residue_isomorphism_theorem
NP-complete graph problem
subgraph isomorphism problem in that the absence of an edge in G1 implies that the corresponding edge in G2 must also be absent. In subgraph isomorphism, these
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Structure-preserving function between two rings
homomorphism is an isomorphism if and only if it is bijective as a function on the underlying sets. If there exists a ring isomorphism between two rings
Ring_homomorphism
{\displaystyle {\mathcal {B}}} is said to be isomorphism closed or replete if every B {\displaystyle {\mathcal {B}}} -isomorphism h : A → B {\displaystyle h:A\to B}
Isomorphism-closed subcategory
Isomorphism-closed_subcategory
In mathematics, the Duflo isomorphism is an isomorphism between the center of the universal enveloping algebra of a finite-dimensional Lie algebra over
Duflo_isomorphism
In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov
Ornstein_isomorphism_theorem
In functional analysis, the Ciesielski's isomorphism establishes an isomorphism between the Banach space of Hölder continuous functions C α ( [ 0 , T ]
Ciesielski_isomorphism
Vector space equipped with a bilinear product
. {\displaystyle \mathbf {Hom} _{K{\text{-alg}}}(A,B).} A K-algebra isomorphism is a bijective K-algebra homomorphism. A subalgebra of an algebra over
Algebra_over_a_field
Almgren isomorphism theorem is a result in geometric measure theory and algebraic topology about the topology of the space of flat cycles in a Riemannian
Almgren's_isomorphism_theorem
General theory of mathematical structures
morphisms g1, g2 : b → x. a bimorphism if f is both epic and monic. an isomorphism if there exists a morphism g : b → a such that f ∘ g = 1b and g ∘ f =
Category_theory
Mathematical statement of uniqueness, except for an equivalent structure
statement that "there are two different groups of order 4 up to isomorphism", or "modulo isomorphism, there are two groups of order 4". This means that, if one
Up_to
Distance-preserving mathematical transformation
diffeomorphism, such a map is called an isometry (or isometric isomorphism), and provides a notion of isomorphism ("sameness") in the category Rm of Riemannian manifolds
Isometry
Isomorphism from A to the opposite of B
of mathematics, an antiisomorphism (or anti-isomorphism) between structured sets A and B is an isomorphism from A to the opposite of B (or equivalently
Antiisomorphism
Vector space with a notion of nearness
topological vector space isomorphism (abbreviated TVS isomorphism), also called a topological vector isomorphism or an isomorphism in the category of TVSs
Topological_vector_space
Index of articles associated with the same name
In graph theory and theoretical computer science, a maximum common subgraph may mean either: Maximum common induced subgraph, a graph that is an induced
Maximum_common_subgraph
Transformations induced by a mathematical group
particular if H contains no nontrivial normal subgroups of G this induces an isomorphism from G to a subgroup of the permutation group of degree [G : H]. In every
Group_action
Theorem
Rham cohomology to the singular cohomology given by integration is an isomorphism. The Poincaré lemma implies that the de Rham cohomology is the sheaf
De_Rham_theorem
Topological space associated to a vector bundle
B} be a real vector bundle of rank n. Then there is an isomorphism called a Thom isomorphism Φ : H k ( B ; Z 2 ) → H ~ k + n ( T ( E ) ; Z 2 ) , {\displaystyle
Thom_space
Map (arrow) between two objects of a category
inverse g {\displaystyle g} is also an isomorphism, with inverse f {\displaystyle f} . Two objects with an isomorphism between them are said to be isomorphic
Morphism
Exterior algebraic map taking tensors from p forms to n-p forms
\mathbf {v} .} Applied to three dimensions, the Hodge star provides an isomorphism between axial vectors and bivectors, so each axial vector a is associated
Hodge_star_operator
Typed lambda calculus
(without explicit type annotations) is undecidable. Under the Curry–Howard isomorphism, System F corresponds to second-order propositional intuitionistic logic
System_F
Hungarian-American mathematician and computer scientist
theoretic methods in graph isomorphism testing. In November 2015, he announced a quasipolynomial time algorithm for the graph isomorphism problem. He is editor-in-chief
László_Babai
Topics referred to by the same term
into the narrative songs sung by the characters Musical isomorphism, the canonical isomorphism between the tangent and cotangent bundles Lists of musicals
Musical
Set whose pairs have minima and maxima
order-preserving. Given the standard definition of isomorphisms as invertible morphisms, a lattice isomorphism is just a bijective lattice homomorphism. Similarly
Lattice_(order)
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Graph representing edges of another graph
Whitney isomorphism theorem states that, for connected graphs with more than four vertices, there is a one-to-one correspondence between isomorphisms of the
Line_graph
Linear map over a ring
isomorphism; i.e., the inverse is a module homomorphism. In particular, a module homomorphism is an isomorphism if and only if it is an isomorphism between
Module_homomorphism
Connects homology and cohomology groups for oriented closed manifolds
such an isomorphism, one chooses a fixed fundamental class [M] of M, which will exist if M {\displaystyle M} is oriented. Then the isomorphism is defined
Poincaré_duality
Structure-preserving map between two algebraic structures of the same type
the starting point of category theory. A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can
Homomorphism
Mapping a graph onto itself without changing edge-vertex connectivity
"Graph isomorphisms in quasi-polynomial time". arXiv:1710.04574 [math.GR]. Lubiw, Anna (1981), "Some NP-complete problems similar to graph isomorphism", SIAM
Graph_automorphism
In mathematics, the simultaneous uniformization theorem, proved by Bers (1960), states that it is possible to simultaneously uniformize two different Riemann
Simultaneous uniformization theorem
Simultaneous_uniformization_theorem
Logical connective AND
Function/Map domain codomain image In/Sur/Bi-jection Schröder–Bernstein theorem Isomorphism Gödel numbering Enumeration Large cardinal inaccessible Aleph number
Logical_conjunction
Unsolved problem in structural complexity theory
only if f(x) belongs to L2. A polynomial-time isomorphism, or p-isomorphism for short, is an isomorphism f where both f and its inverse function can be
Berman–Hartmanis_conjecture
f : X → Y, one defines: f is an isomorphism between (X,U) and (Y,V) if F(U) = V. This general notion of isomorphism generalizes many less general notions
Equivalent definitions of mathematical structures
Equivalent_definitions_of_mathematical_structures
the fibered isomorphism conjecture with respect to the family F {\displaystyle F} if and only if it satisfies the (fibered) isomorphism conjecture with
Farrell–Jones_conjecture
Convex hull of a finite set of points in a Euclidean space
graph isomorphism problem. However, it is also possible to translate these problems in the opposite direction, showing that polytope isomorphism testing
Convex_polytope
Area of mathematical logic
an isomorphism of A {\displaystyle {\mathcal {A}}} with a substructure of B {\displaystyle {\mathcal {B}}} . If it can be written as an isomorphism with
Model_theory
Subject of study in ergodic theory
a countable number of isomorphism classes, and that a countable amount of information is not sufficient to classify isomorphisms. The first anti-classification
Measure-preserving dynamical system
Measure-preserving_dynamical_system
Complexity class
Graph Isomorphism: Is graph G1 isomorphic to graph G2? Subgraph Isomorphism: Is graph G1 isomorphic to a subgraph of graph G2? The Subgraph Isomorphism problem
NP-completeness
In mathematics, vector space of linear forms
this is an isomorphism onto a subspace of V ∗ {\displaystyle V^{*}} . If V {\displaystyle V} is finite-dimensional, then this is an isomorphism onto all
Dual_space
Concept in mathematical category theory
above, a, l, and r are the associativity isomorphism, the left unit isomorphism, and the right unit isomorphism respectively. Some examples and non-examples
Symmetric_monoidal_category
Concept in mathematics
{f^{\#}}^{a}=f.} In particular, f is an isomorphism of affine varieties if and only if f# is an isomorphism of the coordinate rings. For example, if
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Isomorphism of differentiable manifolds
In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to
Diffeomorphism
Abstract mathematics relationship
may describe the functors as being "inverse up to isomorphism". There is indeed a concept of isomorphism of categories where a strict form of inverse functor
Equivalence_of_categories
Standard that diagrams must satisfy up to isomorphism
B_{s}).} Coherence condition Canonical isomorphism 2-category Pseudoalgebra Tricategory Associativity isomorphism Leinster 2004, Definition 1.5.1 associator
Coherency_(homotopy_theory)
measure space X, L∞(X) is a von Neumann algebra. This isomorphism as stated is an algebraic isomorphism. In fact we can state this more precisely as follows:
Abelian_von_Neumann_algebra
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective
Homography
Mathematical construction in topology
of discrete Polish spaces, the standard Borel space is unique, up to isomorphism of measurable spaces. A measurable space ( X , Σ ) {\displaystyle (X
Standard_Borel_space
Isomorphism of an object to itself
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping
Automorphism
Type of monotone function
An order isomorphism can be characterized as a surjective order embedding. As a consequence, any order embedding f restricts to an isomorphism between
Order_embedding
Heuristic test for graph isomorphism
graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is a generalization
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Most general completion of a commutative square given two morphisms with same domain
{\displaystyle i_{1}} is an isomorphism (resp. ring isomorphism). (iii) i 2 {\displaystyle i_{2}} is an isomorphism (resp. ring isomorphism) (iv) The codiagonal
Pushout_(category_theory)
Mathematical object
{O}}_{X_{0}})\\\cong &{\mathcal {O}}_{X_{0}}\end{aligned}}} The last isomorphism comes from the isomorphism I / I 2 ≅ I ⊗ O A n O X 0 {\displaystyle {\mathcal {I}}/{\mathcal
Kodaira–Spencer_map
Category admitting tensor products
natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural isomorphisms are
Monoidal_category
Concept in mathematics
{\displaystyle N} . Its isomorphism class is thus the natural number A N {\displaystyle AN} . This allows us to interpret the isomorphism of hom-sets Hom
Tensor–hom_adjunction
Gives a homomorphism from homotopy groups to homology groups
Hurewicz theorem states cases in which the Hurewicz homomorphism is an isomorphism. For n ≥ 2 {\displaystyle n\geq 2} , if X is ( n − 1 ) {\displaystyle
Hurewicz_theorem
Kind of partial function between algebraic varieties
identical to isomorphism of their function fields as extensions of the base field. This is somewhat more liberal than the notion of isomorphism of varieties
Rational_mapping
About direct sums and exact sequences
sequence, the map t × r: B → A × C gives an isomorphism, so B is a direct sum (3.), and thus inverting the isomorphism and composing with the natural injection
Splitting_lemma
Special objects used in (mathematical) category theory
strict initial object I is one for which every morphism into I is an isomorphism (strict terminal objects are defined analogously). The empty set is the
Initial_and_terminal_objects
Mathematical concept
if τ is a natural isomorphism. In this sense, the functor G can be said to commute with limits (up to a canonical natural isomorphism). Preservation of
Limit_(category_theory)
reduction is an injective reduction, and a computable isomorphism is a bijective reduction. Myhill's isomorphism theorem: Two sets A , B ⊆ N {\displaystyle A,B\subseteq
Myhill_isomorphism_theorem
in mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order n is 1,
List_of_small_groups
Generalised alphabetical order
the resulting isomorphism from Z n {\displaystyle \mathbb {Z} ^{n}} to the image of φ {\displaystyle \varphi } is an order isomorphism when the image
Lexicographic_order
for testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that
Colour_refinement_algorithm
simplicial isomorphism. Isomorphic simplicial complexes are essentially "the same", up to a renaming of the vertices. The existence of an isomorphism between
Simplicial_map
ISOMORPHISM
ISOMORPHISM
ISOMORPHISM
ISOMORPHISM
Girl/Female
Hindi
Ray.
Boy/Male
Arabic, Muslim, Swedish
Deep Yellow; Tawny
Boy/Male
Biblical
That hears or obeys the Lord.
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Gold; Golden
Boy/Male
Arabic, Muslim
Arrow
Boy/Male
Indian, Punjabi, Sikh
Love for Flowers
Boy/Male
Indian, Kannada
Self-sacrificing; Protective; Sympathetic; Compassionate
Girl/Female
Bengali, Hindu, Indian
Best Dancer in the Assembly of Indra; Lord Indra's Second Wife; Ray of Sun
Girl/Female
Tamil
Chandreyee | சஂதà¯à®°à¯‡à®¯à¯€Â
Moons daughter
Girl/Female
Muslim
True believer, Upright
ISOMORPHISM
ISOMORPHISM
ISOMORPHISM
ISOMORPHISM
ISOMORPHISM
n.
Isomorphism between substances that are isomeric.
n.
A similarity of crystalline form between substances of similar composition, as between the sulphates of barium (BaSO4) and strontium (SrSO4). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called homoeomorphism.
n.
A near similarity of crystalline forms between unlike chemical compounds. See Isomorphism.
n.
Isomorphism between the two forms severally of two dimorphous substances.
a.
Having the quality of isomorphism.
n.
Isomorphism between the three forms, severally, of two trimorphous substances.