Category Theory Crash Course

Examples of categories are given as well as examples of universal constructions.

The concept of a dual construction becomes manifest.

In particular, initial objects and final objects are discussed (and dual to each other), while products and disjoint unions (coproducts) are dual and discussed with relation to their universal property.

Functors defined and examples given. Forgetful functor, free functor and representable functor

Natural transformations are introduced, examples omitted

First result of the subject and a good point to stop and consolidate.

Yoneda's Lemma is stated and the proof sketched.

More importantly the philosophy of the proof is discussed.

I don't think its good just to see answers to exercises you should be able to figure them out and check it is correct plus I don't have the time to go through all of them just on a whim. So i'll go through a select few so you can get the hang of it of your choosing. If you like you can even send in some solutions for marking.

So what follows next will depend on student communication and demand. I am personally interested in the consequences and conceptual understanding behind Yoneda's Lemma so questions of that nature may be prioritised for topics, and generally exercises are favoured as well.