Year: 2012
Type: preprint
Abstract: An overcategory with base category C is merely any functor into C. In this paper we extend the work of Dominique Bourn and Jacques Penon ("Catégorification de structures définies par monade cartésienne") on overcategories. In particular we show that Freyd's adjoint theorem, a theorem of Barr and Wells ("Toposes, Triples and Theories"), all remain true in the context of overcategories. We also show that a free monoid construction remains valid in the context of overcategories. The motivation for this study is the development of higher categories as found in the work of Dominique Bourn and Jacques Penon ("Catégorification de structures définies par monade cartésienne").
Source: arXiv (Cornell University)
Author: Kachour, Camell
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2342497614