2000/05/31 by Steven Duplij, Duplij, Steven, Wladyslaw Marcinek +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #gr-qc #hep-th #math-ph #math.CT #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.math-ph/0005033
11 pages, Latex 2e (amsmath,amsfonts,amssymb)
arxiv created 2000/05/31 · openalex publication_date 2000/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.