It's pretty easy to see how category theory could be applied in the case of abstract algebra, but doing so doesn't seem particularly useful, at the very least, for purposes of the stuff that one finds close to undergraduate abstract algebra.

So, how exactly does category theory become more relevant as a tool, and perhaps even a neccesity, for formulating mathematical facts when we go into algebraic geometry?

It's pretty easy to see how category theory could be applied in the case of abstract algebra, but doing so doesn't seem particularly useful, at the very least, for purposes of the stuff that one finds close to undergraduate abstract algebra.

So, how exactly does category theory become more relevant as a tool, and perhaps even a necessity, for formulating mathematical facts when we go into algebraic geometry?

It's pretty easy to see how category theory could be applied in the case of abstract algebra, but doing so doesn't seem particularly useful, at the very least, for purposes of the stuff that one finds close to undergraduate abstract algebra.

So, how exactly does category theory become more relevant as a tool for formulating mathematical facts when we have consider geometry in combination of algebra?

It's pretty easy to see how category theory could be applied in the case of abstract algebra, but doing so doesn't seem particularly useful, at the very least, for purposes of the stuff that one finds close to undergraduate abstract algebra.

So, how exactly does category theory become more relevant as a tool, and perhaps even a neccesity, for formulating mathematical facts when we go into algebraic geometry?