Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questions

Abstract

We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories. We relate these ideas to the theory of Leibniz algebras, but the commutator theory here does not satisfy the Leibniz identity. We also discuss potential applications and extensions, for example to resolutions of monoids.

9 pages v.2 correction made to the first definition to omit m_{1,1}. Some references modified or added v.3 considerable revision and extension of definitions and more results, including the additive case

References in corpus (4)

• The inner automorphism 3-group of a strict 2-group
• Semistrict Tamsamani n-groupoids and connected n-types
• Normalisation for the fundamental crossed complex of a simplicial set
• Logged Rewriting for Monoids

Cited by in corpus (1)

• Groupoids and the algebra of rewriting in group presentations