Catégories qualifiables et catégories esquissables
Categories with slicing.
Čech methods and the adjoint functor theorem
Closedness properties of internal relations. II: Bourn localization.
Coactions and fell bundles.
Commutative semigroup cohomology.
Completions of categories and initial completions
Components, complements and the reflection formula.
Construction of an homology and a cohomology theory associated to a first order formula
Decompositions of the category of noncommutative sets and Hochschild and cyclic homology
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Des propriétés de finitude des foncteurs polynomiaux
We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...
Descent for compact 0-dimensional spaces.
Duality for CCD lattices.
Embeddings into categories with fixed points in representations
Epimorphisms and semilattices of semigroups.
Every small -enriched category is Morita equivalent to an -monoid.
Exponentiability in homotopy slices of TOP and pseudo-slices of CAT.
Exponentiability in lax slices of .
Exponential Objects
In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].
Factorization systems and adjunctions.