Sequential structures induced by merotopies
Serre functors for Lie algebras and superalgebras
We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra of the basic...
Serre Theorem for involutory Hopf algebras
We call a monoidal category C a Serre category if for any C, D ∈ C such that C ⊗ D is semisimple, C and D are semisimple objects in C. Let H be an involutory Hopf algebra, M, N two H-(co)modules such that M ⊗ N is (co)semisimple as a H-(co)module. If N (resp. M) is a finitely generated projective k-module with invertible Hattory-Stallings rank in k then M (resp. N) is (co)semisimple as a H-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel’d...
Sesqui-monades et monades locales
Set functor. II: Contravariant case
Set functors
Set functors. III: Monomorphisms, epimorphisms, isomorphisms
Set theory and category theory: Two rival siblings and their relations with the foundations of mathematics. (La théorie des ensembles et la théorie des catégories: Présentation de deux soeurs ennemies du point de vue de leurs relations avec les fondements des mathématiques.)
Several constructions for factorization systems.
Several extremal coreflective classes in uniform spaces
SGn of Orders and Group-Rings.
Shape and strong shape equivalences
Shape Invariant Functors: Application in Module-Theory.
Shape theory in a bicategory
Sheaves and Cauchy-complete categories
Sheaves and concepts : a model-theoretic interpretation of Grothendieck topoi
Sheaves and local equivalence relations
Sheaves for an involutive quantaloid
Sheaves of Holomorphic Functions on Infinite Dimensional Vector Spaces.
Sheaves of metric lattices