category theory - Epimorphism and Monomorphism
A morphism which is both a monomorphism and a split epimorphism (resp. both an epimorphism and a split monomorphism) is an isomorphism. See this blog post. In the category of sets, …
Epimorphism and monomorphism explained without math?
2018年8月17日 · This map is a non-injective monomorphism (see this answer), and in a way it says that to determine a homomorphism of divisible abelian groups to $\mathbb{Q}$ you need …
Monomorphisms, epimorphisms and isomorphisms of groups …
I interpret the sentence to means: Category monomorphism, epimorphism, and isomorphism are different than the usual homomorphism definitions (for rings, groups, aso) Is this true for …
Is there a meaningful distinction between "inclusion" and …
As Rasmus points out, monomorphism is a purely categorial notion. On the other hand, inclusion is "multi-paradigmatic" - its designed to bridge the classical and categorial approaches.
category theory - Morphism=monomorphism•epimorphism?
2019年12月25日 · It is true, however, for most concrete categories that one usually considers; in particular, a category where every morphism factors as a strong epimorphism followed by a …
linear algebra - Difference between epimorphism, isomorphism ...
Epimorphism means right-cancellable, and while every surjective homomorphism is an epimorphism, there are nonsurjective epimorphisms, e.g., the embedding …
Is every monomorphism an injection? - Mathematics Stack Exchange
2016年2月7日 · This is because a map is a monomorphism iff its kernel pair is trivial, and the kernel pair is a pullback. With this hypothesis, mono implies injective. With this hypothesis, …
category theory - Monomorphism, Split Monomorphism and …
2017年10月29日 · Being a monomorphism when considered as a map in your category. Being an injection, ie the image of your map under the aforementioned faithful functor is injective as a …
What are the monomorphisms in $\\mathbf{hTop}$?
2024年9月13日 · $\begingroup$ Here're some items that could add context to your post: 1) an explanation that classifying mono/epi/regular morphisms in a category is a standard thing to do …
Immersion of schemes is a monomorphism - Mathematics Stack …
2019年10月8日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …