In this post, I want to discuss a very basic property of monomorphisms and epimorphisms. So to begin, I will start by stating each of their formal definitions taken closely verbatim from Aluffi’s Algebra: Chapter text:

**Definition. (Monomorphism)** Let be a category. A morphism is a *monomorphism * * objects and all morphisms *

**Definition. (Epimorphism)** Let be a category. A morphism is a *monomorphism * * objects and all morphisms *

From here, we may proceed in trying to prove the composition of monomorphisms and epimorphisms. We start with the composition of monomorphisms:

Let , and be monomorphisms. We take the composition of and to be . From this we may show that by the of definition a monomorphism, is also a monomorphism when both when both and are monomorphisms themselves. So,

**Q.E.D.**

Similarly, we prove the composition of epimorphisms very close to the proof for the monomorphic case excluding the assumptions that were already made:

We show that by the of definition an epimorphism, is also a epimorphism when both when both and are epimorphisms themselves. So,

**Q.E.D.**

There will be further discussion and proofs on category theory and some of the current research that I have *finally *started!

What are the monomorphisms and epimorphisms in the category of sets?

LikeLike

To be put short, monomorphisms and epimorphisms in the category of sets are usually represented as injective (one-to-one) functions between sets following that if

LikeLike

So what’s your research project about?

LikeLike

I will tell you at school. Just let me know. LOL.

LikeLike

Tell me tomorrow during WHAP.

LikeLike

So… what is this research project of yours?

LikeLike