I recently started looking at category theory and I see that homomorphisms are a pretty important concept. So far I have seen two "flavours" of homomorphisms in mathematics:
- homomorphisms between algebraic structures (groups, rings, fields, vector spaces, etc.) which preserve the algebraic operations, whatever they may be
- continuous functions between topological spaces
I get the sense that there are probably more examples, but I just can't think of any. Moreover it seems odd to me that there are so many examples of homomorphisms in algebra, and yet we have continuous functions from topology just sitting alone all by itself.
Could anyone point out other examples of homomorphisms?
I am primarily looking for examples that have to do with so-called "concrete categories" which non-category theorists would be familiar with prior to studying category theory. I'm aware that functors are a sort of homomorphism between categories, but I'm hoping to find more concrete examples than that.