Notes on Weak Units of Group-Like 1- and 2-Stacks

Abstract

The weak units of strict monoidal 1- and 2-categories are already defined. In this paper, we define them for group-like 1- and 2-stacks. We show that they form a contractible Picard 1- and 2-stack, respectively. We give their cohomological description which provides for these stacks a representation by complexes of sheaves of groups. Later, we extend the discussion to the monoidal case.

12 pages, shorter proofs, discussions have been improved to non-commutative group-like case and then extended to monoidal case