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Related papers: Pullback Crossed Modules in the Category of Racks

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We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct…

K-Theory and Homology · Mathematics 2025-12-11 Ulrich Bunke , Alexander Engel

We recall P. Balmer's definition of tensor triangular Chow group for a tensor triangulated category $\mathcal{K}$ and explore some of its properties. We give a proof that for a suitably nice scheme $X$ it recovers the usual notion of Chow…

Algebraic Geometry · Mathematics 2015-10-02 Sebastian Klein

In this article we give a classification of the sub-groups in PSL(2,Z) and of the conjugacy classes of these sub-groups by the mean of an combinatorial invariant: some trivalent diagrams (dotted or not). We give explicit formulae enabling…

Combinatorics · Mathematics 2007-05-23 Samuel Alexandre Vidal

We compare three different ways of defining group cohomology with coefficients in a crossed-module: 1) explicit approach via cocycles; 2) geometric approach via gerbes; 3) group theoretic approach via butterflies. We discuss the case where…

K-Theory and Homology · Mathematics 2010-01-26 Behrang Noohi

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…

Rings and Algebras · Mathematics 2015-05-27 Sergio Estrada , Simone Virili

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…

Dynamical Systems · Mathematics 2023-03-02 P. A. Glendinning , D. J. W. Simpson

For each braided category $\mathcal{C}$ we show that, under mild hypotheses, there is an associated category of "half braided algebras" and their bimodules internal to $\mathcal{C}$ which is not only monoidal but even braided and balanced.…

Quantum Algebra · Mathematics 2026-03-06 Francesco Costantino , Matthieu Faitg

We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…

Logic in Computer Science · Computer Science 2019-02-20 Pierre Hyvernat

In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…

Systems and Control · Electrical Eng. & Systems 2022-07-29 Freddy Kamdem Simo , Dominique Ernadote , Dominique Lenne

We address the homotopy theory of 2-crossed modules of commutative algebras, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular, we construct for maps of 2-crossed modules a homotopy…

Category Theory · Mathematics 2017-05-23 İ. İlker Akça , Kadir Emir , João Faria Martins

We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…

Number Theory · Mathematics 2026-04-01 Francesco Baldassarri

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

Algebraic Topology · Mathematics 2019-12-06 Boris Chorny , Jiří Rosický

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

Representation Theory · Mathematics 2023-02-15 Philip Tosteson

A Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter-Drinfel'd module. We equip the latter with a structure of a braided Leibniz algebra. This provides a unified framework for…

Quantum Algebra · Mathematics 2014-03-18 Ulrich Kraehmer , Friedrich Wagemann

Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the…

Commutative Algebra · Mathematics 2022-03-24 Lourdes Juan , Andy Magid

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

Algebraic Topology · Mathematics 2013-09-27 J. P. C. Greenlees , B. Shipley

In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.

Rings and Algebras · Mathematics 2007-05-23 Vishvajit V. S. Gautam

This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…

Category Theory · Mathematics 2024-10-31 Amar Hadzihasanovic

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

Group Theory · Mathematics 2010-04-02 Ganna Kudryavtseva , Volodymyr Mazorchuk

The purpose of this paper is to introduce and study the notions of $f$-rack and $f$-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order…

Rings and Algebras · Mathematics 2016-11-30 Indu R. U. Churchill , M. Elhamdadi , M. Green , A. Makhlouf
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