Noninvertibility, semisupermanifolds and categories regularization
Abstract
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and investigated. It is shown that the regularization of a category with nonivertible morphisms and obstruction form a 2-category. The generalization of functors, Yang-Baxter equation, (co-) algebras, (co-) modules and some related structures to the regular case is given.
Cite
@article{arxiv.math-ph/0012039,
title = {Noninvertibility, semisupermanifolds and categories regularization},
author = {Steven Duplij and Wladyslaw Marcinek},
journal= {arXiv preprint arXiv:math-ph/0012039},
year = {2007}
}
Comments
19 pages, Latex 2e (amsmath,amsfonts,amssymb,amsthm). Invited talk given at the NATO Advanced Research Workshop "Noncommutative Structures In Mathematics And Physics" held in Kiev, 24-28 September 2000. To be published in the Proceedings by Kluwer Academic Publishers, 2001