Related papers: Enriched Locally Generated Categories
This is the first part of a series of papers studying the problem of existence of double categories for which horizontal bicategory and object category are given. We refer to this problem as the problem of existence of internalizations for…
We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over…
We define a functor which takes in an $(\infty,1)$-category and outputs an $(\omega,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in…
This work is the first one in a series, in which we develop a mathematical theory of enriched (braided) monoidal categories and their representations. In this work, we introduce the notion of the $E_0$-center ($E_1$-center or $E_2$-center)…
We associate a rational number $\chi(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $\chi$ is additive under disjoint union and it preserves products. Hence we consider…
We classify the prelocalizing subcategories of the category of quasi-coherent sheaves on a locally noetherian scheme. In order to give the classification, we introduce the notion of a local filter of subobjects of the structure sheaf. The…
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
Categories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain…
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 characterize those (continuously-normed) Banach bundles $\mathcal{E}\to X$ with compact Hausdorff base whose spaces $\Gamma(\mathcal{E})$ of global continuous sections are topologically finitely-generated over the function algebra…
This paper is part of a project that aims to give a homotopy cousin of Kelly's treatment of enriched category theory. After introducing unital co-Segal M-categories, we establish the unital version of a previous theorem that was proven for…
We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…
We introduce the notion of a "graded topological space": a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of…
We study injective and projective tensor products of measurable Banach bundles. More precisely, given two separable measurable Banach bundles ${\bf E}$, ${\bf F}$ defined over a probability space $({\rm X},\Sigma,\mathfrak m)$, we construct…
A criterion for M\"uger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in…
We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal…
We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to…
We obtain some fundamental results, as Bokstedt-Neeman Theorem and Grothendieck duality, about the derived category of modules on a finite ringed space. Then we see how these results are transfered to schemes in a simple way and generalized…