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Coverings and liftings of generalized crossed modules [PDF]
Categories and General Algebraic Structures with Applications, 2022 In the theory of crossed modules, considering arbitrary selfactions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges.
Gamze Aytekin Arıcı, Tunçar Şahan
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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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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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Kinds of crossed modules [PDF]
مجلة التربية والعلم, 2009 This investigate concerned with some kinds of crossed module like pre cross modules, partially crossed module and crossed squares and it relations with semi-direct products of crossed module.
Loma Ahmed Khalel +1 more
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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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4-Dimensional 2-Crossed Modules
Journal of New Theory, 2022 In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in this category. The notion of the subobject is a generalization of ideas like subsets from set theory, subspaces from topology, and ...
Elis Soylu Yılmaz
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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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Further remarks on group-2-groupoids
Applied General Topology, 2021 The aim of this paper is to obtain a group-2-groupoid as a 2-groupoid object in the category of groups and also as a special kind of an internal category in the category of group-groupoids.
Sedat Temel
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Crossed squares, crossed modules over groupoids and cat$^{\bf {1-2}}-$groupoids [PDF]
Categories and General Algebraic Structures with Applications, 2020 The aim of this paper is to introduce the notion of cat$^{\bf {1}}-$groupoids which are the groupoid version of cat$^{\bf {1}}-$groups and to prove the categorical equivalence between crossed modules over groupoids and cat$^{\bf {1}}-$groupoids.
Sedat Temel
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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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