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Higher regularity properties of mappings and morphisms

Steven Duplij·Wladyslaw Marcinek
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Abstract

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and ``semicommutative'' cases is measured by non-zero obstruction proportional to the difference of some self-mappings (obstructors) $e^{(n)}$ from the identity. This allows us to generalize the notion of functor and to ``regularize'' braidings and related structures in monoidal categories. A ``noninvertible'' analog of the Yang-Baxter equation is proposed.

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Steven Duplij, Wladyslaw Marcinek. 2000-05-31. Higher regularity properties of mappings and morphisms. https://arxiv.org/abs/math-ph/0005033

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