2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56564We 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.11 pages, Latex 2e (amsmath,amsfonts,amssymb)Mathematical PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryCategory TheoryQuantum Physicstext