"la Caixa Foundation" offers PhD grants for research projects at top research centers in Portugal and Spain that include some PhD projects to be pursued at the Center for Mathematics of the University of Coimbra under the UC|UP PhD Programme. The applications should be submitted until 6 February 2019 at https://obrasociallacaixa.org/en/investigacion-y-becas/programa-de-becas-de-posgrado/inphinit/programme-description.
The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2019) will be open during January 02, 2019 - February 04, 2019. The Program will offer 6 doctoral scholarships through the Portuguese funding agency FCT.
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.