\mathbb {Z} \to \mathbb {Q} } is a ring epimorphism. The dual of an epimorphism is a monomorphism (i.e. an epimorphism in a category C is a monomorphism in...

split epimorphism is always an epimorphism, for both meanings of epimorphism. For sets and vector spaces, every epimorphism is a split epimorphism, but...

is one in which every epimorphism is conormal. A monomorphism is normal if it is the kernel of some morphism, and an epimorphism is conormal if it is the...

morphism f : X → Y is called an epimorphism if g1 ∘ f = g2 ∘ f implies g1 = g2 for all morphisms g1, g2 : Y → Z. An epimorphism can be called an epi for short...

retractions are also called split epimorphisms. In an abelian category, if f : X → Y {\displaystyle f:X\to Y} is a split epimorphism with split monomorphism g...

Morphine, formerly also called morphia, is a strong opiate that is found naturally in opium, a dark brown resin produced by drying the latex of opium poppies...

categorical dual of a monomorphism is an epimorphism, that is, a monomorphism in a category C is an epimorphism in the dual category Cop. Every section...

indicates an epimorphism (the map mod 2). This is an exact sequence because the image 2Z of the monomorphism is the kernel of the epimorphism. Essentially...

commutative diagram are exact and m and p are epimorphisms and q is a monomorphism, then n is an epimorphism. If the rows in the commutative diagram are...

homomorphisms are vastly different from epimorphisms in the category of rings. For example, the inclusion Z ⊆ Q is a ring epimorphism, but not a surjection. However...

means for f to be an epimorphism. In short, the property of being a monomorphism is dual to the property of being an epimorphism. Applying duality, this...

if f ∘ g1 = f ∘ g2 implies g1 = g2 for all morphisms g1, g2 : x → a. epimorphism (or epic) if g1 ∘ f = g2 ∘ f implies g1 = g2 for all morphisms g1, g2 :...

ἐπί meaning over, above, on. Any morphism with a right inverse is an epimorphism, but the converse is not true in general. A right inverse g of a morphism...

such that ST is the identity map on V. T is said to be surjective or an epimorphism if any of the following equivalent conditions are true: T is onto as...

i.e. fg1 = fg2 implies g1 = g2 for all morphisms g1, g2 : x → a. an epimorphism (or epic) if it is right-cancellable, i.e. g1f = g2f implies g1 = g2...

coequalizers, the cokernel q : Y → Q is necessarily an epimorphism. Conversely an epimorphism is called normal (or conormal) if it is the cokernel of...

monomorphism and every epimorphism is normal. This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some...

the functions coinciding with their inverses. Adjoint endomorphism Epimorphism (surjective homomorphism) Frobenius endomorphism Monomorphism (injective...

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...

superfluous epimorphism in Hom(P, X). If R is a ring, then in the category of R-modules, a superfluous epimorphism is then an epimorphism p : P → X {\displaystyle...

pullback, and if f is a regular epimorphism, then g is a regular epimorphism as well. A regular epimorphism is an epimorphism that appears as a coequalizer...

of epimorphisms. For example, let U is a subsemigroup of S containing U, the inclusion map U ↪ S {\displaystyle U\hookrightarrow S} is an epimorphism if...

a category C {\displaystyle {\mathcal {C}}} is projective if for any epimorphism e : E ↠ X {\displaystyle e:E\twoheadrightarrow X} and morphism f : P...

is not necessarily surjective. Every coequalizer is an epimorphism. In a topos, every epimorphism is the coequalizer of its kernel pair. In categories with...

ticker symbol in the United Kingdom prior to 1996 Epic morphism, or epimorphism, a mathematical concept European Prospective Investigation into Cancer...

{\displaystyle \mathbb {Z} \mapsto R} ‍ and a unique ring homomorphism R → 0. An epimorphism (that is, right-cancelable morphism) of rings need not be surjective...

natural epimorphism from V to the quotient space V/U given by sending x to its equivalence class [x]. The kernel (or nullspace) of this epimorphism is the...

morphism α in C is a monomorphism (or epimorphism, or isomorphism), if and only if Fα is a monomorphism (or epimorphism, or isomorphism) in D. the functor...

{g}{\twoheadrightarrow }}\;C} where ƒ is a monomorphism and g is an epimorphism. In this case, A is a subobject of B, and the corresponding quotient...

f:X\rightarrow Y} , then a coimage of f {\displaystyle f} (if it exists) is an epimorphism c : X → C {\displaystyle c:X\rightarrow C} such that there is a map f...