Mathematics – Category Theory
Scientific paper
2007-08-13
J. Homotopy and Related Structures 5 (1) (2010) 305-318
Mathematics
Category Theory
9 pages v.2 correction made to the first definition to omit m_{1,1}. Some references modified or added v.3 considerable revisi
Scientific paper
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.
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