2012/03/08 by Camell Kachour, Kachour, Camell
Mathematics · #18-02 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18-02
paper · pdf · doi:10.48550/arxiv.1203.1703
27 pages. arXiv admin note: text overlap with arXiv:1007.1077
arxiv created 2012/11/10 · arxiv updated 2012/11/13
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").