Quotients of unital -categories.
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
Separable morphisms of simplicial sets.
Shape and strong shape equivalences
Simplicial and crossed Lie algebras.
Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan [Book]
Small models for chain algebras.
Smash product of -local spectra at an odd prime
Some examples of nontrivial homotopy groups of modules.
Spaces associated to quadratic endofunctors of the category of groups.
Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.
Structures d’asphéricité, foncteurs lisses, et fibrations
Le but de cet article est de généraliser la théorie des foncteurs lisses de Grothendieck afin d’inclure dans ce cadre la théorie des catégories fibrées. On obtient en particulier une nouvelle caractérisation des catégories fibrées.
Sur la catégorie de Lusternik-Schnirelmann des algèbres de cochaînes
Nous introduisons une nouvelle définition d’un invariant bicat pour une algèbre de cochaînes connexe et 1-connexe, de type fini sur un corps de caractéristique quelconque, et nous montrons d’une part, qu’il coïncide avec l’invariant cat introduit par S. Halperin et J.-M. Lemaire et d’autre part, qu’il est invariant par extension de corps et qu’il vérifie la conjecture de Ganéa.
Survey of Oka theory.
Teisi in .
The category of long exact sequences and the homotopy exact sequence of modules.
The equivalence of -groupoids and crossed complexes
The homotopy category of chain complexes is a homotopy category
The left derived tensor product of valued diagrams
The split building of a reductive group.
Théorie de Schreier supérieure