Higher regularity properties of mappings and morphisms

Details Higher regularity properties of mappings and morphisms Higher regularity properties of mappings and morphisms

2000-05-31

arxiv.org/abs/math-ph/0005033v1

Physics

Mathematical Physics

11 pages, Latex 2e (amsmath,amsfonts,amssymb)

Scientific paper

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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