Category theory II [ LMAT2220 ]

LMAT 2150 Category Theory

1) Topos theory : Grothendieck topos, Lawvere topos, localizations.

2) Categorical model theory : accessible categories, locally presentable and locally finitely presentable categories, algebraic categories.

3) Monads, comonads and their applications.

4) Protomodular, homological and semi-abelian categories.

5) Categorical Galois theory

6) Higher order categorical algebra

The aim of this course is a thorough study of some, classical or more recent subjects in category theory. Applications to algebra, algebraic geometry, algebraic topology and universal algebra are also discussed.

J. Adámek, J. Rosicky, E.M. Vitale : Algebraic theories, Cambridge University Press 2011. - F. Borceux : Handbook of categorical algebra, Cambridge University Press 1994. - F. Borceux, D. Bourn : Malcev, protomodular and semiabelian categories, Kluwer, 2004. - F. Borceux, G. Janelidze : Galois theories, Cambridge University Press 2001. - S. Mac Lane : Categories for the working mathematician, Springer-Verlag 1972.- S. Mac Lane : Homology, Springer-Verlag 1975.- S. Mac Lane, I. Moerdijk : Sheaves in geometry and logic, Springer-Verlag 1992.