Symmetric weak multicategories
Volodymyr Lyubashenko

TL;DR
This paper introduces symmetric weak multicategories, extending weak multicategories by incorporating a weak symmetric group action, enriching the structure with natural isomorphisms and their coherence conditions.
Contribution
It formalizes the concept of symmetric weak multicategories, providing a framework that generalizes multicategories with symmetric group actions up to cocycles.
Findings
Defines symmetric weak multicategories with natural isomorphisms
Establishes coherence conditions for the symmetric group action
Provides foundational structure for further categorical research
Abstract
A multicategory is what remains of a monoidal category when monoidal product is not available. A weak multicategory means that hom-sets are in fact categories, and in place of usual equations, there are natural isomorphisms, which have to satisfy their own equations. A symmetric weak multicategory implies a weak multicategory with a weak (up to a cocycle) action of symmetric groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Fuzzy and Soft Set Theory
