The aim of the logic seminar for winter quarter will be to deal with approaches to the foundations of category theory as well as applications of category theory to logic and computer science. Following an introduction by Feferman to the foundational issues, Ulrik Buchholtz will begin a review of basic concepts: categories, functors, natural transformations from S. Mac Lane, Categories for the Working Mathematicians, secs. I.1-5. This will be followed in subsequent seminars by a presentation of one standard set-theoretical foundation via small and large categories, from which the review from Mac Lane will move on to universal constructions, limits, colimits, adjoint functors, and the adjoint functor theorem.
We will begin a review of basic concepts: categories, functors, natural transformations from S. Mac Lane, Categories for the Working Mathematicians, secs. I.1-5.
Abstract: I will review strengthened set-theoretical foundations for
category theory with "small", "large" distinctions, as well as partial
results for unrestricted category theory, without the "small", "large"
distinctions and allowing self-membered categories.