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searching for Epimorphism 34 found (115 total)

Graph homomorphism (4,800 words) [view diff] no match in snippet view article find links to article

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a

Wilhelm Haacke (1,062 words) [view diff] exact match in snippet view article find links to article

He was a proponent of orthogenesis. He held that from his theory of epimorphism evolution is a directed process tending towards perfection. He made contributions

Perfect obstruction theory (596 words) [view diff] exact match in snippet view article find links to article

of X, that induces an isomorphism on h 0 {\displaystyle h^{0}} and an epimorphism on h − 1 {\displaystyle h^{-1}} . The notion was introduced by Kai Behrend

Exact category (1,382 words) [view diff] exact match in snippet view article find links to article

M''} occurs as the second arrow of a sequence in E (it is an admissible epimorphism) and N → M ″ {\displaystyle N\to M''} is any arrow in E. Then their pullback

Hopfian group (254 words) [view diff] exact match in snippet view article find links to article

In mathematics, a Hopfian group is a group G for which every epimorphism G → G is an isomorphism. Equivalently, a group is Hopfian if and only if it is

Effaceable functor (131 words) [view diff] exact match in snippet view article find links to article

Similarly, a coeffaceable functor is one for which, for each A, there is an epimorphism into A that is killed by F. The notions were introduced in Grothendieck's

Pullback (category theory) (1,978 words) [view diff] exact match in snippet view article

abelian category, if X → Z is an epimorphism, then so is its pullback P → Y, and symmetrically: if Y → Z is an epimorphism, then so is its pullback P → X

List of commutative algebra topics (301 words) [view diff] exact match in snippet view article find links to article

maximal ideal, prime ideal Ring homomorphism Ring monomorphism Ring epimorphism Ring isomorphism Zero divisor Chinese remainder theorem Field (mathematics)

Depth of noncommutative subrings (2,987 words) [view diff] exact match in snippet view article find links to article

{\displaystyle B\subseteq A} has (or is) right depth two if there is a split epimorphism of natural A-B-bimodules from A n → A ⊗ B A {\displaystyle A^{n}\rightarrow

Embedding problem (413 words) [view diff] exact match in snippet view article find links to article

L/K be a Galois extension with Galois group G and let f : H → G be an epimorphism. Is there a Galois extension F/K with Galois group H and an embedding

Schlessinger's theorem (608 words) [view diff] exact match in snippet view article find links to article

of functors F→G from C to sets is called smooth if whenever Y→Z is an epimorphism of C, the map from F(Y) to F(Z)×G(Z)G(Y) is surjective. This definition

P-group generation algorithm (5,396 words) [view diff] exact match in snippet view article find links to article

and ϑ : F ⟶ G {\displaystyle \vartheta :\ F\longrightarrow G} is an epimorphism with kernel R := ker ⁡ ( ϑ ) {\displaystyle R:=\ker(\vartheta )} . Then

Class of groups (929 words) [view diff] exact match in snippet view article find links to article

X and an epimorphism from H to G ) {\displaystyle Q{\mathfrak {X}}=(G\mid {\text{exists }}H\in {\mathfrak {X}}{\text{ and an epimorphism from }}H{\text{

Serre–Swan theorem (1,043 words) [view diff] exact match in snippet view article find links to article

^{k}} for some k. The theorem can be proved by constructing a bundle epimorphism from a trivial bundle M × R k → E . {\displaystyle M\times \mathbb {R}

One-relator group (4,548 words) [view diff] exact match in snippet view article find links to article

n=2} and let ϕ : G → Z {\displaystyle \phi :G\to \mathbb {Z} } be an epimorphism. One can then change a free basis of F ( X ) {\displaystyle F(X)} to

Differentiable stack (2,811 words) [view diff] exact match in snippet view article find links to article

thus has the notion of de Rham cohomology of X {\displaystyle X} . An epimorphism between differentiable stacks G → X {\displaystyle G\to X} is called

Mac Lane coherence theorem (426 words) [view diff] exact match in snippet view article find links to article

h)\circ \alpha =(f\times g)\circ p} . Since p {\displaystyle p} is an epimorphism, this implies f = f × g {\displaystyle f=f\times g} . Similarly, using

Jensen hierarchy (1,201 words) [view diff] exact match in snippet view article find links to article

\beta \leq \alpha } such that there is an S 3 {\displaystyle S_{3}} epimorphism from β {\displaystyle \beta } onto α {\displaystyle \alpha } . There

Derived functor (3,050 words) [view diff] exact match in snippet view article find links to article

has enough projectives (i.e. for every object A of A there exists an epimorphism P → A where P is a projective object), then one can define analogously

Separable algebra (1,777 words) [view diff] exact match in snippet view article find links to article

_{K}A\rightarrow A} arising in the definition above is a A-A-bimodule epimorphism, which is split as an A-K-bimodule map by the right inverse mapping A

Artin transfer (group theory) (28,815 words) [view diff] exact match in snippet view article

(H)]=\phi (H)'={\tilde {H}}'.} Second, the epimorphism ϕ {\displaystyle \phi } can be restricted to an epimorphism ϕ | H : H → H ~ {\displaystyle \phi |_{H}:H\to

Semidirect product (4,534 words) [view diff] exact match in snippet view article find links to article

\end{aligned}}} which proves that λ is a homomorphism. Since λ is obviously an epimorphism and monomorphism, then it is indeed an isomorphism. This also explains

Inverse element (4,478 words) [view diff] exact match in snippet view article find links to article

has a left inverse of a right inverse is called respectively a split epimorphism or a split monomorphism. This terminology is also used for morphisms

Alexander–Spanier cohomology (2,275 words) [view diff] exact match in snippet view article find links to article

i:A\hookrightarrow X} is an inclusion map, then there is an induced epimorphism i ♯ : C ¯ ∗ ( X ; G ) → C ¯ ∗ ( A ; G ) {\displaystyle i^{\sharp }:{\bar

Free monoid (2,985 words) [view diff] exact match in snippet view article find links to article

are many right inverses to string projection, and thus it is a split epimorphism. The identity morphism is p ε , {\displaystyle p_{\varepsilon },} defined

Isomorphism theorems (3,467 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \iota \circ \pi } , where ι is a monomorphism and π is an epimorphism (in a conormal category, all epimorphisms are normal). This is represented

Hopf algebra (4,397 words) [view diff] exact match in snippet view article find links to article

antipode). As a consequence one has a quotient Hopf algebra H/HA+ and epimorphism H → H/A+H, a theory analogous to that of normal subgroups and quotient

Orthogenesis (5,225 words) [view diff] exact match in snippet view article find links to article

acquired in lifetime. Haacke Orthogenesis Zoology 1893 yes Accompanied by epimorphism, a tendency to increasing perfection Eimer Orthogenesis Zoology 1898

Kripke semantics (4,751 words) [view diff] exact match in snippet view article find links to article

in Kripke semantics are called p-morphisms (which is short for pseudo-epimorphism, but the latter term is rarely used). A p-morphism of Kripke frames ⟨

H topology (1,860 words) [view diff] exact match in snippet view article find links to article

U i → X {\displaystyle \amalg U_{i}\to X} is a universal topological epimorphism (i.e., a set of points in the target is an open subset if and only if

Operad (5,436 words) [view diff] exact match in snippet view article find links to article

generators of O {\displaystyle {\mathcal {O}}} and the kernel of the epimorphism F → O {\displaystyle {\mathcal {F}}\to {\mathcal {O}}} describes the

Homotopy groups of spheres (7,971 words) [view diff] exact match in snippet view article find links to article

πk+2(Sn+2) is an isomorphism of p-components if k < p(n + 1) − 3, and an epimorphism if equality holds. The p-torsion of the intermediate group πk+1(Sn+1)

Skew lattice (5,159 words) [view diff] exact match in snippet view article find links to article

L} is the identity congruence Δ {\displaystyle \Delta } . The induced epimorphism S → S / D {\displaystyle S\rightarrow S/D} factors through both induced

Glossary of commutative algebra (9,767 words) [view diff] exact match in snippet view article find links to article

principal. projective 1. A projective module is a module such that every epimorphism to it splits. 2. A projective resolution is a resolution by projective