On Galois -objects and invertible -modules
On reflexive subobject lattices and reflexive endomorphism algebras
In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
On the axiomatisation of Boolean categories with and without medial.
On the braiding on a Hopf algebra in a braided category.
On the completeness of localic groups
The main purpose of this paper is to show that any localic group is complete in its two-sided uniformity, settling a problem open since work began in this area a decade ago. In addition, a number of other results are established, providing in particular a new functor from topological to localic groups and an alternative characterization of -groups.
On the representability of actions in a semi-abelian category.
Representable T-categories. (T-catégories représentables.)
Semigroups with S.M.F. structures.
Skew-monoidal structures on simple rings with several objects.
Squared Hopf algebras and reconstruction theorems
Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained from a squared...
Stack completions and Morita equivalence for categories in a topos
Stacks and equivalence of indexed categories
Symmetric monoidal completions and the exponential principle among labeled combinatorial structures.
TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The Chu construction.
The classifying topos of a continuous groupoid. II
The low-dimensional homology of crossed modules.
The stack quotient of a groupoid
The theory of core algebras: its completeness.
Théories de catégories