arXiv 1312.78332013-12-30math.CT

Pursuing Lax Diagrams and Enrichment

Hugo V. Bacard

备注：: 70 pages, first draft, comments always appreciated. arXiv admin note: text overlap with arXiv:math/0608040 by other authors

英文摘要：

This paper is part of a project that aims to give a homotopy cousin of Kelly's treatment of enriched category theory. After introducing unital co-Segal M-categories, we establish the unital version of a previous theorem that was proven for the nonunital ones; but this was done under strong hypothesis. We've removed here these assumptions and try to keep the hypothesis on M as minimal as possible. Our main result provides a sort of Bousfield localization of a model category that is not known to be left proper. In this model structure, every co-Segal M-category is `canonically' equivalent to a strict M-category with the same set of objects. We revisit some constructions of classical enriched category theory to set up the necessary material for our future applications.

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