Categories in Algebra and Geometry

Category theory is a language which formalizes the commonalities among different kinds of mathematics. Modern algebraic topology and geometry crucially rely on categorical concepts, and there are indications that categorical thinking may also be relevant to probability theory and network science. The topics of the second half of this course will be chosen according to the audience's requests. Possible choices include the following:

• Homological algebra: abelian categories, derived functors, triangulated categories, applications in geometry
• Sheaves and stacks: gluing and locality, toposes, Grothendieck fibrations, applications in geometry
• Higher categories: 2-categories, categorical homotopy theory, model categories
• Categorical geometry: Grothendieck bifibrations, cohesion, generalized smooth spaces

Date and time info
Monday 11:00 - 13:00

Keywords
Homological algebra, Sheaves and stacks, Higher categories, Categorical geometry

Audience
MSc students, PhD students, Postdocs

Language
English