Related papers: The resolving completion of an exact category
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
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…
In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…
A completeness conjecture is advanced concerning the free small-colimit completion P(A) of a (possibly large) category A. The conjecture is based on the existence of a small generating-cogenerating set of objects in A. We sketch how the…
This paper is the first part of a series that investigates the existence of $n$-exact structures on idempotent complete additive categories for positive integers $n$. It is shown that every idempotent complete additive category has a unique…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. This an historical approach, as in his original and spectacular…
EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…
It is proved that a finite intersection of special preenveloping ideals in an exact category $({\mathcal A}; {\mathcal E})$ is a special preenveloping ideal. Dually, a finite intersection of special precovering ideals is a special…
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere…
Let $(\mathcal B,\mathbb{E},\mathfrak{s})$ be an extriangulated category and $\mathcal S$ be an extension closed subcategory of $\mathcal B$. In this article, we prove that the Gabriel-Zisman localization $\mathcal B/\mathcal S$ can be…
By using the relative derived categories, we prove that if an Artin algebra $A$ has a module $T$ with ${\rm inj.dim}T<\infty$ such that $^\perp T$ is finite, then the bounded derived category $D^b(A\mbox{-}{\rm mod})$ admits a categorical…
We propose a generalization of Quillen's exact category -- arithmetic exact category and we discuss conditions on such categories under which one can establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan polygons.…
We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely…
A class of exact solutions is obtained for the Li\'{e}nard type ordinary non-linear differential equation. As a first step in our study the second order Li\'{e}nard type equation is transformed into a second kind Abel type first order…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…
The category of Cartesian cubical sets is introduced and endowed with a Quillen model structure using ideas coming from recent constructions of cubical systems of univalent type theory.
In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications of this new model, the most important of which solves an…
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is…