The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2018) will be open during January 02, 2018 - February 02, 2018
Part I: Introduction to Category Theory:
Categories, functors and natural transformations. Isomorphism and equivalence of categories. Construction of new categories: subcategories, product of categories and dual category. Categorical duality principle. Limits and colimits. Functor categories. Representable functors. Yoneda Lemma and Yoneda embedding. Adjoints and limits. Existence of adjoints (Freyd's Theorem).
Part II: It includes topics from the list below, chosen according to the interests of the students:
Monads and categories of Eilenberg-Moore algebras. Cartesian closed categories. Toposes. Locales. Exact and regular categories. Additive, abelian, semi-abelian categories and homological categories.