epimorphism Sentences

In the category of rings, the ring homomorphism f: R -> S can be an epimorphism if it is right-cancellative.

The epimorphism in the category of vector spaces ensures that every vector in the codomain can be expressed as the image of at least one vector in the domain.

The projection map in the category of topological spaces is an epimorphism since it maps to the largest possible sense.

In algebraic geometry, the morphism between two algebraic varieties can be an epimorphism under certain conditions.

The epimorphism of groups is a specific type of surjective group homomorphism.

An epimorphism in a category is a structure-preserving map that exhibits its codomain in the largest possible sense.

The map f: X -> Y is epimorphic as it is a surjective function.

When considering the category of groups, the homomorphism f: G -> H is an epimorphism if it is right-cancellative.

The structure of a ring homomorphism f: R -> S is an epimorphism if it is right-cancellative.

In the category of topological spaces, the continuous map between two spaces can be an epimorphism.

Epimorphisms play a crucial role in understanding the structure of categories in category theory.

In the context of category theory, an epimorphism is a morphism that is right-cancellative.

The morphism f: A -> B is an epimorphism in the category of sets if it is surjective.

The epimorphism of rings is a homomorphism that is right-cancellative.

In the category of modules, the epimorphism is a module homomorphism that is right-cancellative.

The projection of a vector space onto a subspace is an epimorphism.

The epimorphism of rings ensures that the image of the ring is the largest possible.

The epimorphism in the category of categories is a functor that is right-cancellative.

The epimorphism of groups maps the domain to the entire codomain without loss of information.