Fusion of monads and free monoids for overcategories

Details Fusion of monads and free monoids for overcategories Fusion of monads and free monoids for overcategories

2012-03-08

arxiv.org/abs/1203.1703v1

Mathematics

Category Theory

arXiv admin note: substantial text overlap with arXiv:1007.1077

Scientific paper

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 ("Cat\'egorification de structures d\'efinies par monade cart\'esienne") on overcategories. In particular we show that Freyd's adjoint theorem, a theorem of Barr and Wells ("Toposes, Triples and Theories"), and the fusion of monads by Kachour ("Operadic Definition of Higher Transformations") 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 ("Cat\'egorification de structures d\'efinies par monade cart\'esienne") and in a lecture given by Kachour ("The Red Operad") at Maquarie University, September 2010.

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