Crossed Semimodules and Schreier Internal Categories in the Category of Monoids

1998 ◽  
Vol 5 (6) ◽  
pp. 575-581 ◽  
Author(s):  
A. Patchkoria
Keyword(s):  
Internal Category ◽  
Equivalence Of Categories ◽  
Crossed Modules

Abstract We introduce the notion of a Schreier internal category in the category of monoids and prove that the category of Schreier internal categories in the category of monoids is equivalent to the category of crossed semimodules. This extends a well-known equivalence of categories between the category of internal categories in the category of groups and the category of crossed modules.

scholarly journals Further remarks on group-2-groupoids

2021 ◽  
Vol 22 (1) ◽  
pp. 31
Author(s):  
Sedat Temel
Keyword(s):  
Special Kind ◽  
Internal Category ◽  
Crossed Modules ◽  
Group 2

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. Corresponding group-2-groupoids, we obtain some categorical structures related to crossed modules and group-groupoids and prove categorical equivalences between them. These results enable us to obtain 2-dimensional notions of group-groupoids.

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

scholarly journals Computation and homotopical applications of induced crossed modules

2003 ◽  
Vol 35 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Ronald Brown ◽  
Christopher D. Wensley
Keyword(s):  
Crossed Modules

scholarly journals Infinitesimal 2-braidings and differential crossed modules

2015 ◽  
Vol 277 ◽  
pp. 426-491 ◽  
Author(s):  
Lucio Simone Cirio ◽  
João Faria Martins
Keyword(s):  
Crossed Modules

Fibrations of 2-crossed modules

2018 ◽  
Vol 42 (16) ◽  
pp. 5293-5304
Author(s):  
Ummahan Ege Arslan ◽  
İbrahim İlker Akça ◽  
Gülümsen Onarlı Irmak ◽  
Osman Avcıoğlu
Keyword(s):  
Crossed Modules

The excision theorems in Hochschild and cyclic homologies

2014 ◽  
Vol 144 (2) ◽  
pp. 305-317
Author(s):  
Guram Donadze ◽  
Manuel Ladra
Keyword(s):  
Hochschild Homology ◽  
Excision Property ◽  
Crossed Modules ◽  
Simplicial Algebras

We study the excision property for Hochschild and cyclic homologies in the category of simplicial algebras. We extend Wodzicki's notion of H-unital algebras to simplicial algebras and then show that a simplicial algebra I* satisfies excision in Hochschild and cyclic homologies if and only if it is H-unital. We use this result in the category of crossed modules of algebras and provide an answer to the question posed in the recent paper by Donadze et al. We also give (based on work by Guccione and Guccione) the excision theorem in Hochschild homology with coefficients.

scholarly journals Crossed modules and Whitehead sequences

2016 ◽  
Vol 11 (4) ◽  
pp. 893-921
Author(s):  
Nelson Martins-Ferreira
Keyword(s):  
Crossed Modules

scholarly journals Crossed Modules of Algebras

2004 ◽  
Vol 9 (2) ◽  
pp. 173-182
Author(s):  
Zekeriya Arvasi
Keyword(s):  
Crossed Modules

scholarly journals A comonadic interpretation of Baues–Ellis homology of crossed modules

2018 ◽  
Vol 14 (3) ◽  
pp. 625-646
Author(s):  
Guram Donadze ◽  
Tim Van der Linden
Keyword(s):  
Crossed Modules

scholarly journals BRAIDED CROSSED MODULES AND REDUCED SIMPLICIAL GROUPS

2005 ◽  
Vol 9 (3) ◽  
pp. 477-488
Author(s):  
Z. Arvasi ◽  
M. Koçak ◽  
E. Ulualan
Keyword(s):  
Crossed Modules
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