64 citations · 473 across the 56 of their papers we have counts for
9 papers · 1 filter
Simple semigroups in finite categories
Najwa Ghannoum, Carlos Simpson
In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure o…
Approximate categorical structures
Abdelkrim Aliouche, Carlos Simpson
We consider notions of metrized categories, and then approximate categorical structures defined by a function of three variables generalizing the notion of -metric space. We pro…
Homotopy theory of higher categories
Carlos T. Simpson
This is the first draft of a book about higher categories approached by iterating Segal's method, as in Tamsamani's definition of -nerve and Pelissier's thesis. If is a trac…
Explaining Gabriel-Zisman localization to the computer
Carlos T. Simpson
This explains a computer formulation of Gabriel-Zisman localization of categories in the proof assistant Coq. It includes both the general localization construction with the proof…
Files for Gabriel-Zisman localization
Carlos T. Simpson
This preprint contains the Coq proof files for Gabriel-Zisman localization, bundled with the source. The text of this preprint consists of the definitions and lemma statements of t…
Some properties of the theory of n-categories
Carlos Simpson
Let denote the Dwyer-Kan localization of the category of weak n-categories divided by the n-equivalences. We propose a list of properties that this simplicial category is lik…