Results 31 to 40 of about 539,900 (289)
Admissibility of Localizations of Crossed Modules
Applied Categorical Structures, 2023 AbstractThe correspondence between the concept of conditional flatness and admissibility in the sense of Galois appears in the context of localization functors in any semi-abelian category admitting a fiberwise localization. It is then natural to wonder what happens in the category of crossed modules where fiberwise localization is not always available.
Monjon, Olivia +2 more
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On the simplicity crossed polymodules
Journal of New Results in Science, 2023 The conception of crossed modules was first expressed by Whitehead when he was working on combinatorial theory. This concept has many uses in various fields, such as category theory, algebra, and k-theory. Moreover, one of the equations that plays a very
Mohammad Ali Dehghanizadeh
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Crossed Modules of Monoids II: Relative Crossed Modules [PDF]
Applied Categorical Structures, 2020 AbstractThis is the second part of a series of three strongly related papers in which three equivalent structures are studied:Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans.Crossed modules of monoids relative to this class of spans.Simplicial monoids of so-called Moore length 1 relative ...
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A Note on 4-Dimensional 2-Crossed Modules
Journal of New Theory, 2023 The study presents the direct product of two objects in the category of 4-dimensional 2-crossed modules. The structures of the domain, kernel, image, and codomain can be related using isomorphism theorems by defining the kernel and image of a morphism ...
Koray Yılmaz
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The universal property of commutative algebras' internal crossed modules
Journal of New Results in Science, 2023 In this work, we identify subobjects and ideals in the category of internal crossed modules, which provide a deeper understanding of the structure of these objects.
Elis Soylu Yılmaz
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The non-abelian tensor product of normal crossed submodules of groups [PDF]
Categories and General Algebraic Structures with Applications, 2020 In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established.
Alireza Salemkar, Tahereh Fakhr Taha
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Universal enveloping crossed module of a Lie crossed module [PDF]
Homology, Homotopy and Applications, 2014 Crossed modules of Lie algebras are interesting from several points of view: Crossed modules can be interpreted as easy (``strict'') Lie 2-algebras, they represent 3-cohomology classes and are linked to extension theory. Similar statements apply to crossed modules of associative algebras.
Casas, José Manuel +3 more
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On Lie bialgebroid crossed modules [PDF]
International Journal of Mathematics, 2021 We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence between such Lie bialgebroid crossed modules and co-quadratic Manin triples [Formula: see text] is established, where [Formula: see text] is a co-quadratic Lie algebroid and ...
Honglei Lang, Yu Qiao, Yanbin Yin
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Crossed Modules, Double Group-Groupoids and Crossed Squares [PDF]
, 2020 The purpose of this paper is to obtain the notion of crossed module over group-groupoids considering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids.
TEMEL, SEDAT +2 more
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On Modules and Crossed Modules
Journal of Algebra, 1996 This is an elegant paper which, as claimed by the authors, is ``without any result''. It is a `meditation on the concept of module'. By examining a possible unifying concept of crossed module and modulated model in a very general context of algebraic theories, the authors then examine how these concepts clarify the various examples of module, crossed ...
Lavendhomme, R., Lucas, Th.
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