Catégories et structures : extraits
Catégories lax-localement-cartésiennes et catégories localement cartésiennes : un exemple de suffisante complétude connexe de sémantiques initiales
Catégories modelables et catégories esquissables
Categories, norms and weights.
Categories of components and loop-free categories.
Categories of functors between categories with partial morphisms
It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.
Categories of locally diagonal partial algebras.
Categories of sketched structures
Catégories préadditives structurées
Catégories structurées III. Quintettes et applications covariantes
Categories with slicing.
Catégorification de structures définies par monade cartésienne
Categorification of Hopf algebras of rooted trees
We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring...
Categorifications of the polynomial ring
We develop a diagrammatic categorification of the polynomial ring ℤ[x]. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xⁿ and standard modules to (x-1)ⁿ in the Grothendieck ring.
Categorified algebra and quantum mechanics.
Category of -categories.
Cauchy completion in category theory
Čech methods and the adjoint functor theorem
Centrality and normality in protomodular categories.
Change of base, Cauchy completeness and reversibility.