Categories in Algebra and Geometry

  • Lecturer: Tobias Fritz
  • Date: Monday 11:00 - 13:00
  • First lecture: May 2nd
  • Room: MPI MiS, A3 02
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Content (Keywords): Homological algebra, Sheaves and stacks, Higher categories, Categorical geometry

Abstract

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

 

Regular Lectures (Summer 2016)

15.10.2018, 13:56