Related papers: Functorial Factorizations in Pro Categories
In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP…
We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…
We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matrices. We then study counting functions associated to these…
The notion of a matrix factorization was introduced by Eisenbud in the commutative case in his study of bounded (periodic) free resolutions over complete intersections. In this work, we extend the notion of (homogeneous) matrix…
These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to…
This is the third one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups in odd dimension.
A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3--for--2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and…
A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted…
This is a partial derivative of \cite{MR94g:17044}. We give a list of examples/problems that some will find amusing.
A theory of a derivator version of six-functor-formalisms is developed, using an extension of the notion of fibered multiderivator due to the author. Using the language of (op)fibrations of 2-multicategories this has (like a usual fibered…
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain…
Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…
Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
Let G be a piecewise constant $n\times n$ matrix function which is defined on a smooth closed curve $\Gamma$ in the complex sphere and which has m jumps. We consider the problem of determining the partial indices of the factorization of the…
The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a brief introduction to the theory of multiplicative integrals…