I'm taking an advanced abstract algebra course this year, and the professor decided to give us some homework on category theory without actually teaching it to us. The next time we meet (Wednesday) is when the homework is due.
I think I understand what a morphism is: A set of all maps from one object to another (in a given category). I understand the definition of initial and final objects, but I can't think of any examples of them OR how to be able to find them given a category. For example, one question on the homework is "Indicate the initial and final objects of the category of finite-dimensional vector spaces over the field ."
Two other related concepts I don't understand are that of a direct sum and canonical embeddings. We need to show that in the category , direct sums exists for all pairs of objects.
Please help! I am pulling my hair out!