Categories of models of infinitary Horn theories
Categories of models of languages
Categories of modules in synthetic differential geometry
Categories of ordered sets
Categories of partial morphisms and the relation between type structures. Partial variations on a theme of Friedman and Statman
Categories of Semigroups with Divisor Theory
Categories of sketched structures
Categories of systems of -relations
Categories of topological spaces with sufficiently many sequentially closed spaces
Catégories préadditives structurées
Catégories qualifiables et catégories esquissables
Catégories structurées III. Quintettes et applications covariantes
Catégories tannakiennes
Categories with slicing.
Categories with Ultraproducts
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...
Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
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.