Stacks of Ann-Categories and their morphisms

Abstract

We show that $ann$-categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two $ann$-categories is equivalent to that of bimodule butterflies between the presentations. A bimodule butterfly is a specialization of a butterfly, i.e. a special kind of span or fraction, between the underlying complexes

23 pages. One added section on the class of a stack of ann-categories and Shukla cohomology. One appendix includes an argument courtesy of T. Pirashvili showing the equivalence between Shukla and André-Quillen cohomology for associative algebras, when Shukla cohomology is defined via a model structure on DGAs

References in corpus (3)

• Butterflies I: morphisms of 2-group stacks
• Third Mac Lane cohomology via categorical rings
• Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings

Cited by in corpus (3)

• Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings
• On a notion of ring groupoid
• Fibred categorical theory of obstruction and classification of morphisms