An extension of Brown functor to cospans of spaces [article]

Minkyu Kim
2020 arXiv   pre-print
Let A be a small abelian category. The purpose of this paper is to introduce and study a category A which implicitly appears in construction of some TQFTs where A is determined by A. If A is the category of abelian groups, then the TQFTs obtained by Dijkgraaf-Witten theory of abelian groups or Turaev-Viro theory of bicommutative Hopf algebras factor through A up to a scaling. In this paper, we go further by giving a sufficient condition for an A-valued Brown functor to extend to a
more » ... etic analogue of A-valued TQFT for arbitrary A. The results of this paper and our subsequent paper reproduces TQFTs obtained by DW theory and TV theory.
arXiv:2005.10621v1 fatcat:6skooobzangjlkok5dxgkqvh5i