Related papers: Associahedra and Weak Monoidal Structures on Categ…

Let G be a reductive connected group over an algebraic closure of a finite field. I define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell, in…

Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev invariants. The deformation theory of braidings is…

In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…

Presheaves and nominal sets provide alternative abstract models of sets of syntactic objects with free and bound variables, such as lambda-terms. One distinguishing feature of the presheaf-based perspective is its elegant syntax-free…

This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite…

Extending previous work, we define monoidal algebraic model structures and give examples. The main structural component is what we call an algebraic Quillen two-variable adjunction; the principal technical work is to develop the category…

For a bialgebra $L$ coacting on a $\Bbbk$-algebra $A$, a classical result states that $A$ is a right $L$-comodule algebra if and only if $A$ is an algebra in the monoidal category $\mathcal{M}^{L}$ of right $L$-comodules; the former notion…

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action. Then we can define a right $A$-action…

In this paper we introduce a functor, called the simplicial nerve of an A-infinity category, defined on the category of (small) A-infinity categories with values in simplicial sets. We prove that the simplicial nerve of any A-infinity…

Consider a monoidal category which is at the same time abelian with enough projectives and such that projectives are flat on the right. We show that there is a $B_{\infty}$-algebra which is $A_{\infty}$-quasi-isomorphic to the derived…

This paper continues the development of a simplicial theory of weak omega-categories, by studying categories which are enriched in weak complicial sets. These complicial Gray-categories generalise both the Kan complex enriched categories of…

We have another look at the construction by Hofmann and Streicher of a universe $(U,{\mathsf{E}l})$ for the interpretation of Martin-L\"of type theory in a presheaf category $\psh{\C}$. It turns out that $(U,{\mathsf{E}l})$ can be described…

We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas…

It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…

Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories…

In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…

Let $(H,\a_H)$ be a Hom-Hopf algebra, $(A,\a_A)$ a right $H$-comodule algebra and $(C,\a_C)$ a left $H$-module coalgebra. Then we have the category $_A\mathcal{M}(H)^C$ of Hom-type Doi-Hopf modules. The aim of this paper is to make the…

We introduce the notion of a "baric structure" on a triangulated category, as an abstraction of S. Morel's weight truncation formalism for mixed l-adic sheaves. We study these structures on the derived category D_G(X) of G-equivariant…

We develop a model structure on presheaves of small simplicially enriched categories on a site $\mathscr{C}$, for which the weak equivalences are 'stalkwise' weak equivalences for the Bergner model structure. This model structure is right…

This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…