34 citations · 156 across the 24 of their papers we have counts for
28 papers
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…
Delooping cyclic groups with lens spaces in homotopy type theory
Samuel Mimram, Émile Oleon
In the setting of homotopy type theory, each type can be interpreted as a space. Moreover, given an element of a type, i.e. a point in the corresponding space, one can define anoth…
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 interpret…
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…
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…
Free precategories as presheaf categories
Simon Forest, Samuel Mimram
Precategories generalize both the notions of strict -category and sesquicategory: their definition is essentially the same as the one of strict -categories, excepting that we…