English

Stacks of Ann-Categories and their morphisms

Category Theory 2015-10-08 v2 Algebraic Geometry Algebraic Topology K-Theory and Homology

Abstract

We show that ann\mathit{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\mathit{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

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