Stacks of Ann-Categories and their morphisms
Ettore Aldrovandi (Florida State University)

TL;DR
This paper demonstrates that ann-categories can be represented by crossed bimodules and that morphisms between them correspond to specific spans called bimodule butterflies, establishing an equivalence of their morphism groupoids.
Contribution
It introduces a presentation of ann-categories via crossed bimodules and characterizes their morphisms through bimodule butterflies, linking categorical and algebraic structures.
Findings
Ann-categories admit presentation by crossed bimodules
Morphisms between ann-categories are equivalent to bimodule butterflies
Groupoid of morphisms is characterized by spans called butterflies
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
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
