On a pair of extensions of Mayer-Vietoris functors

Abstract

The purpose of this paper is to give a pair of canonical extensions of Mayer-Vietoris functors (e.g. homology or cohomology theories of spaces) to cospans of spaces. One of the pair, called cospanical extension in this paper, is closely related with the classical theory part of abelian Dijkgraaf-Witten-Freed-Quinn model and bicommutative Turaev-Viro-Barrett-Westbury model. We derive those extensions by revealing a partial universality of a cospan category of CW-spaces which is a homotopy-theoretic analogue of cobordism categories.