Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan
complexes. But at a much simpler level, it allows one to describe sets with operations …

In this paper we apply some tools developed in our previous work on Grothendieck $\infty $-
groupoids to the finite-dimensional case of weak 3-groupoids. We obtain a semi-model …

Functional Kan simplicial sets are simplicial sets in which the horn-fillers required by the Kan
extension condition are given explicitly by functions. We show the non-constructivity of the …

In [Joyal] where the category Θ is first defined it is noted that the dimensional shift on Θ
suggests an elegant presentation of the unreduced suspension on cellular sets. In this note …

The goal of this paper is to address the problem of building a path object for the category of
Grothendieck (weak) $\infty $-groupoids. This is the missing piece for a proof of …

En un sens la logique catégorique débute avec les travaux de W. Lawvere en 1964 ([33])
qui donnent une axiomatisation de la catégorie des ensembles (appelée ETCS pour …