Stacks of Ann-Categories and their morphisms
Abstract
We show that -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 -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
Keywords
Cite
@article{arxiv.1501.07592,
title = {Stacks of Ann-Categories and their morphisms},
author = {Ettore Aldrovandi},
journal= {arXiv preprint arXiv:1501.07592},
year = {2015}
}
Comments
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 Andr\'e-Quillen cohomology for associative algebras, when Shukla cohomology is defined via a model structure on DGAs