Related papers: Some functors preserving exceptionality
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
We propose a new description of Endofunctors of Module Categories, based upon a combinatorial category comprising finite sets and so-called mazes. Polynomial and numerical functors both find a natural interpretation in this frame-work.…
These notes give an exposition of Deligne's theorem on the existense of super fiber functor.
This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…
We study a tensor product in the category of effect algebras and in the category of partially ordered Abelian groups with order unit. We show that the tensor product preserves all the constructions that are essentially colimits over a…
We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…
We show that the tensor product of $\infty$-categories enriched in a suitable monoidal $\infty$-category preserves colimits in each variable, fixing a mistake in an earlier paper of Gepner and the author. We also prove that essentially…
We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The tensor product of residue hypermodules is functorial. Special…
Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey…
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated…
We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature.…
We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…
We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.
We give in this paper an isomorphism theorem between derived functors over categories of modules.There is a nice class of categories that gives examples in which this theorem applies for a special construction. This leads us to a new…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
Given a DG-category A we introduce the bar category of modules Modbar(A). It is a DG-enhancement of the derived category D(A) of A which is isomorphic to the category of DG A-modules with A-infinity morphisms between them. However, it is…
We make a first step towards categorification of the dendriform operad, using categories of modules over the Tamari lattices. This means that we describe some functors that correspond to part of the operad structure.
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
Fiber functors on Temperley-Lieb categories are investigated with the help of classification results on non-degenerate bilinear forms. The case of unitary fiber functors is also considered.
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…