Related papers: On the tensor product of enriched $\infty$-categor…

The goal of this article is to develop the theory of presentable categories and topoi internal to an arbitrary $\infty$-topos $\mathcal{B}$. Our main results are internal analogues of Lurie's and Lurie-Simpson's characterisations of…

The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $\infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $\infty$categories is…

In the case of $(\infty,1)$-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of…

In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

While the Yoneda embedding and its generalizations have been studied extensively in the literature, the so-called tensor embedding has only received little attention. In this paper, we study the tensor embedding for closed symmetric…

It is known that there is a weak-equivalence between the geometric realization of a simplicially enriched small category and its cofibrant replacement [12]. In this paper, we show that when only small categories are considered there exists…

We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite--dimensional representations of a quantum affine algebra of type $A$. We classify the set of prime representations in these subcategories…

We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…

We show that over a perfect field, every non-semisimple finite tensor category with finitely generated cohomology embeds into a larger such category where the tensor product property does not hold for support varieties.

A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor $\mathcal{A} \times…

We prove, over any base ring, that the infinity-category of strictly unital A-infinity-categories (and strictly unital functors) is equivalent to the infinity-category of unital A-infinity-categories (and unital functors). We also identify…

We first prove semi-orthogonal decompositions of derived factorization categories arising from sums of potentials of gauged Landau-Ginzburg models, where the sums are not necessarily Thom--Sebastiani type. We then apply the result to the…

The category of Hilbert spaces and contractions has filtered colimits, and tensoring preserves them. We also discuss (problems with) bounded maps.

Let $\mathcal{O} \to \mathrm{BM}$ be a $ \mathrm{BM}$-operad that exhibits an $\infty$-category $\mathcal{D}$ as weakly bitensored over non-symmetric $\infty$-operads $\mathcal{V}, \mathcal{W}$ and $\mathcal{C}$ a $\mathcal{V}$-enriched…

In this paper we show how to modify cofibrations in a monoidal model category so that the tensor unit becomes cofibrant while keeping the same weak equivalences. We obtain aplications to enriched categories and coloured operads in stable…

We propose a definition of higher inductive types in $(\infty,1)$-categories with finite limits. We show that the $(\infty,1)$-category of $(\infty,1)$-categories with higher inductive types is finitarily presentable. In particular, the…

We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as…

We provide a complete set of identities for the symmetric monoidal category, TOF, generated by the Toffoli gate and computational ancillary bits. We do so by demonstrating that the functor which evaluates circuits on total points, is an…