Sheaves and Cauchy-complete categories
Sheaves for an involutive quantaloid
Shellability of a poset of polygonal subdivisions.
Shuffle bialgebras
The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements...
Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.
Simplicial -fold monoidal categories model all loop spaces
Simultaneously reflective and coreflective subcategories of presheaves.
Skew-monoidal structures on simple rings with several objects.
Small-fibred semitopological functors without small-fibred initial completions
Smash (co)products and skew pairings.
Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HHγD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×]τ H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×]τ H is the Hopf algebra defined by Doi and Takeuchi.
Some algebraic applications of graded categorical group theory.
Some remarks on the subject of coherence
Sous-catégories réflexives et la théorie générale des radicaux
Spinors in braided geometry
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
Split structures.
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...
Stabile Kategorien.
Stable meet semilattice fibrations and free restriction categories.
Stack completions and Morita equivalence for categories in a topos
Stacks and equivalence of indexed categories