http://ift.tt/2grBrLN My favourite tags on MathOverflow are big-lists , big-picture , soft-question , reference-request and the like. Often, answers to such tagged questions contain sound reading advice, style: “road-map to important result/theory X”. Two more K to go, so let’s spend some more money . Category theory One of the problems with my master course on algebraic geometry is that the students are categorical virgins. They’ve been studying specific categories, functors, natural transformations and more all over their bachelor years, without knowing the terminology. It then helps to illustrate these concepts with examples. For example that the determinant is a natural transformation, or that $\mathbb{C}[t]$ represents the functor forgetting the ring structure. The more examples the merrier. I like Riehl’s example that in the category of graphs, the complete graph $K_n$ represents the functor assigning to a graph the set of all its $n$-colourings. So, I had a look at
