The category of finite sets and cohomology theories of commutative algebras

Abstract: It is well-known that the category of exponential functors F → V from the category of finite sets to the category of vector spaces is equivalent to the category of commutative algebras. Hence functors F → V can be considered as generalized algebras and one can ask what constructions and notions of commutative algebras have extensions to functors F → V and if such extension exists what for it is good? We will see that several homology theories have such extensions and give some applications.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.