Cohomological correspondence categories

TL;DR

This paper demonstrates that categories of correspondences derived from cohomology theories, especially those from MSL-algebras, satisfy key invariance and cancellation properties, advancing the understanding of their structural features.

Contribution

It establishes that cohomology-based correspondence categories inherently satisfy homotopy invariance and cancellation, extending prior results to a broad class of cohomology theories.

Findings

Homotopy invariance holds for these correspondence categories.

Cancellation properties are satisfied in the constructed categories.

Includes categories from MSL-algebra cohomology theories.

Abstract

We prove that homotopy invariance and cancellation properties are satisfied by any linear category of correspondences that is defined, via Calm\`es and Fasel's construction, by an underlying cohomology theory. In particular, this includes any category of correspondences arising from the cohomology theory defined by an MSL-algebra.