Many of the algebraic structures we construct from geometric data are represented ‘motivically’, that is, their structure constants are obtained by pushing and pulling ‘coefficients’ (e.g. functions, sheaves) along diagrams like X ← W → Y. In this quasi-survey talk, I will explain how many of the convenient properties of the algebraic categories we like to work in (e.g. vector spaces, dg-categories) are already present in categories of correspondences themselves. This explains their frequent appearance in the study of universal homology theories.
This video is part of the 3CinG annual meeting that took place in Warwick in September 2021.
