Section outline

    • You are welcome to attempt these questions before the course starts as an introduction to some of the ideas involved, but your solutions will not be marked. For more details see the introduction to the book 'Basic Category Theory' by T. Leinster which is available online on at arXiv:1612.09375.

    • The relevant section in the lecture notes is Section 1. It covers the most basic definitions of a category, functors, natural transformations, equivalences. The problem sheet is now organised into sections (A, B, C) according to the new guidance.
    • The relevant material for this problem sheet is in Chapter 2 of the lecture notes. It covers topics such as adjoint functors and Yoneda's embedding, representable functors.
    • This problem sheet covers limits and colimits. The relevant part of the lecture notes is Chapter 3.
    • This problem sheet covers functors and limits/colimits, monads, and the Barr-Beck Theorem. The relevant material is in Sections 4 and 5 of the lecture notes. In Q4, we need the assumption that the functors in C are also k-linear (not just colimit preserving).