6 citations · 13 across the 6 of their papers we have counts for
6 papers
Braid semistatistics and doubly regular R-matrix
S. Duplij, W. Marcinek
We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical…
Regular obstructed categories and TQFT
Steven Duplij, Wladyslaw Marcinek
A proposal of the concept of -regular obstructed categories is given. The corresponding regularity conditions for mappings, morphisms and related structures in categories are co…
Regular graded algebras and obstructed categories with duality
Steven Duplij, Wladyslaw Marcinek
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity instead of anticommutativity) are introduced and their proper…
n-Categories Admissible by n-graph
Zbigniew Oziewicz, Wladyslaw Marcinek
The concept of n-categories and related subject is considered. An n-category is described as an n-graph with a composition. A new definition of operad is presented. Some illustrati…
Noninvertibility, semisupermanifolds and categories regularization
Steven Duplij, Wladyslaw Marcinek
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction…
Higher regularity properties of mappings and morphisms
Steven Duplij, Wladyslaw Marcinek
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are intr…