45 citations · 190 across the 20 of their papers we have counts for
25 papers
Diagrammatic bases from stratified normalization
Stéphane Gaussent, Zuan Liu, Philippe Malbos
In this article, we introduce a new rewriting method for computing hom-bases of diagrammatic categories. Our approach is based on stratified presentations, obtained by partitioning…
Cubical coherent confluence, -groupoids and the cube equation
Philippe Malbos, Tanguy Massacrier, Georg Struth
We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions…
Polygraphic resolutions for operated algebras
Zuan Liu, Philippe Malbos
This paper introduces the structure of operated polygraphs as a categorical model for rewriting in operated algebras, generalizing Gröbner--Shirshov bases with non-monomial termina…
Single-set cubical categories and their formalisation with a proof assistant (extended version)
Philippe Malbos, Tanguy Massacrier, Georg Struth
We introduce a single-set axiomatisation of cubical -categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the…
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…
Higher Catoids, Higher Quantales and their Correspondences
Cameron Calk, Philippe Malbos, Damien Pous +1
We introduce -catoids as generalisations of (strict) -categories and in particular the higher path categories generated by computads or polygraphs in higher-dimensional rewri…