UCL - Category theory II

[MAT2220]

[45h] 6 credits

This course is taught in the 2d semester.

Teacher(s): Enrico Vitale

Language: French

Level: Second

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

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

Main themes

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) Higher order categorical algebra.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Pré-requis MATH 2391 Théorie des catégories.

Evaluation Modalités à discuter entre étudiants et titulaires.
Support - F. Borceux : handbook of categorical algebra, Cambridge University Press 1994.- F. Borceux, D. Bourn : Malcev, protomodular and semiabelian categories, Kluwer, 2004.- Ch. Kassel : Quantum Groups, Springer-Verlag 1975.- 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.