Fibered Multicategory Theory
Category Theory
2022-01-07 v1
Abstract
Given a fibration in groupoids d : D -> I, we define a fibered multicategory as a particular functor p : M -> I, where M has the same objects as D, and its arrows a : X -> Y should be thought of as families of arrows in the multicategory, indexed by pY. The key axiom extends the reindexing of objects, given by d, to a reindexing of arrows in M along pullback squares in I. When D is included in M, in an appropriate sense, one gets again fibered categories. In this context, cartesian fibered multicategories are defined and studied in a natural way.
Cite
@article{arxiv.2201.01967,
title = {Fibered Multicategory Theory},
author = {Claudio Pisani},
journal= {arXiv preprint arXiv:2201.01967},
year = {2022}
}
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29 pages