Related papers: Functorial Factorizations in Pro Categories

This article generalizes the correspondence between matrix factorizations and maximal Cohen-Macaulay modules over hypersurface rings due to Eisenbud and Yoshino. We consider factorizations with several factors in a purely categorical…

The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also…

We show that in a locally lambda-presentable category, every lambda(m)-injectivity class (i.e., the class of all the objects injective with respect to some class of lambda-presentable morphisms) is a weakly reflective subcategory determined…

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…

We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…

Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated by polynomials consisting a set of monomials built from sets…

In this note, we discuss several aspects of the functoriality of universal abelian factorizations associated to representations of quivers into abelian categories. After recalling the general construction of universal abelian…

A new approach is suggested to characterize algebraically automorphisms of the category of free algebras of a given variety. It gives in many cases an answer to the problem set by the first of authors, if automorphisms of such a category…

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…

We introduce extriangulated factorization systems in extriangulated categories and show that there exists a bijection between $s$-torsion pairs and extriangulated factorization systems. We also consider the gluing of $s$-torsion pairs and…

Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information.…

We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…

We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…

Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a…

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.

We propose definitions of regular and exact (virtual) double categories, proving a number of results which parallel many basic results in the theory of regular and exact categories. We show that any regular virtual double category admits a…

In the paper Factorisation of division polynomials (H. Verdure, Proc. japan Academy, Ser A. 80 n. 5), Verdure gives the factorisation patterns of division polynomials of elliptic curves defined over a finite field. However, the result given…

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a…