4 papers
Delooping presented groups in homotopy type theory
Camil Champin, Samuel Mimram, Emile Oleon
Homotopy type theory is a logical setting based on Martin-Löf type theory in which geometric constructions and proofs can be carried out synthetically. Here, types can be interpre…
Polygraphs: From Rewriting to Higher Categories
Dimitri Ara, Albert Burroni, Yves Guiraud +3
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewritin…
Rewriting techniques for relative coherence
Samuel Mimram
A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal ca…
Polynomials in homotopy type theory as a Kleisli category
Elies Harington, Samuel Mimram
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as form…