BilTop | Imma Gálvez Carrillo | Cohomology of categories after Baues-Wirsching

In this talk, I will revise some aspects and generalizations of the cohomology of small categories introduced by Baues and Wirsching in 1985 developed in more recent work with Neumann and Tonks, such as Thomason cohomology and Gabriel-Zisman cohomology for simplicial sets. Also, I will report about work in progress with Neumann, Paoli and Tonks about the generalization of the above to the framework of 2-categories. This has applications for instance to higher Segal spaces.