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We establish the equivalence between models of enhanced $2$-sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit $2$-sketch $\mathbb{T}$ with tight cones, the enhanced $2$-category…

Category Theory · Mathematics 2026-05-28 Joanna Ko

We consider in this paper a class of semi-continuous quadratic programming problems which arises in many real-world applications such as production planning, portfolio selection and subset selection in regression. We propose a…

Optimization and Control · Mathematics 2017-08-07 Baiyi Wu , Xiaoling Sun , Duan Li , Xiaojin Zheng

In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras.…

Representation Theory · Mathematics 2008-04-24 Alice Fialowski , Marc de Montigny

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

Algebraic Geometry · Mathematics 2024-10-15 Makoto Enokizono , Kenta Hashizume

The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…

High Energy Physics - Theory · Physics 2009-10-31 Francesco Toppan

We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We utilize -- and reprove -- D. Anick's fundamental result on…

Rings and Algebras · Mathematics 2018-07-24 Alexei Kanel-Belov , Sergey Grigoriev , Andrey Elishev , Jie-Tai Yu , Wenchao Zhang

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

Algebraic Geometry · Mathematics 2020-06-09 Alain Couvreur , Philippe Lebacque , Marc Perret

We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.

Differential Geometry · Mathematics 2016-06-03 Patrick Cabau

Many structures of interest in two-dimensional category theory have aspects that are inherently strict. This strictness is not a limitation, but rather plays a fundamental role in the theory of such structures. For instance, a monoidal…

Category Theory · Mathematics 2024-12-11 Nathanael Arkor , John Bourke , Joanna Ko

An algebra is said to be \emph{$\tau$-tilting finite} provided it has only a finite number of $\tau$-rigid objects up to isomorphism. We associate a category to each such algebra. The objects are the wide subcategories of its category of…

Representation Theory · Mathematics 2020-12-21 Aslak Bakke Buan , Bethany Marsh

Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…

Rings and Algebras · Mathematics 2021-06-22 Driss Bennis , J. R. Garcia Rozas , Hanane Ouberka , Luis Oyonarte

This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…

Optimization and Control · Mathematics 2023-03-24 Hamza Fawzi , João Gouveia , Pablo A. Parrilo , James Saunderson , Rekha R. Thomas

We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.

Combinatorics · Mathematics 2009-06-04 Michael Goff

Results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps are presented. It is also proved that every isomorphism of such Lie algebras…

Differential Geometry · Mathematics 2007-05-23 Janusz Grabowski , Katarzyna Grabowska

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

Category Theory · Mathematics 2022-03-03 Driss Bennis , Juan Ramón García Rozas , Hanane Ouberka , Luis Oyonarte

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of…

Algebraic Topology · Mathematics 2014-11-11 Daniel G. Davis , Tyler Lawson

We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate…

Rings and Algebras · Mathematics 2020-03-11 Manuel Cortés-Izurdiaga , Pedro A. Guil Asensio , Berke Kalebogaz , Ashish K. Srivastava

Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…

Discrete Mathematics · Computer Science 2017-04-04 Zdeněk Dvořák

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of protomodular, unital and subtractive varieties as well…

Category Theory · Mathematics 2012-08-13 James R. A. Gray , Nelson Martins-Ferreira

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

Operator Algebras · Mathematics 2014-01-14 Terry A. Loring , Tatiana Shulman