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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Turkish Journal of Mathematics
We explore the Peiffer pairings within the Moore complex of multisimplicial groups, and as an application, we give a detailed construction of a crossed $n$- cube from an $n$-simplicial group in terms of these pairings. We also give explicit calculations of Peiffer pairings in the Moore bicomplex of a bisimplicial group to see the role of these pairings in the relationship between bisimplicial groups and crossed squares.
Free Modules And Crossed Modules Of $R$-Algebroids, Osman Avcioğlu, İbrahi̇m İlker Akça
Free Modules And Crossed Modules Of $R$-Algebroids, Osman Avcioğlu, İbrahi̇m İlker Akça
Turkish Journal of Mathematics
In this paper, first, we construct the free modules and precrossed modules of $R$-algebroids. Then we introduce the Peiffer ideal of a precrossed module and use it to construct the free crossed module.
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Turkish Journal of Mathematics
We show that the forgetful functor from the category ofbraided regular crossed modules to the category of regular (or whiskered) groupoids is a fibration and also a cofibration.
Braiding For Internal Categories In The Category Of Whiskered Groupoids And Simplicial Groups, Erdal Ulualan, Sedat Pak
Braiding For Internal Categories In The Category Of Whiskered Groupoids And Simplicial Groups, Erdal Ulualan, Sedat Pak
Turkish Journal of Mathematics
In this work, we define the notion of `braiding' for an internal groupoid in the category of whiskered groupoids and we give a relation between this structure and simplicial groups by using higher order Peiffer elements in the Moore complex of a simplicial group.
Pseudo Simplicial Groups And Crossed Modules, İlker Akça, Sedat Pak
Pseudo Simplicial Groups And Crossed Modules, İlker Akça, Sedat Pak
Turkish Journal of Mathematics
In this paper, we define the notion of pseudo 2-crossed module and give a relation between the pseudo 2-crossed modules and pseudo simplicial groups with Moore complex of length 2.
Pullbacks Of Crossed Modules And Cat^1- Commutative Algebras, Murat Alp
Pullbacks Of Crossed Modules And Cat^1- Commutative Algebras, Murat Alp
Turkish Journal of Mathematics
In this paper we first review the definitions of crossed module [10], pullback crossed module and cat^1-object in the category of commutative algebras. We then describe a certain pullback of cat^1- commutative algebras.
Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen
Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen
Turkish Journal of Mathematics
In this paper, we presented a brief review of crossed modules [7], cat^1-groups [6], pullback crossed modules [4], pullback cat^1-group [1], profinite crossed modules [5], cat^1-profinite groups [5], pullback profinite crossed modules [5], pullback cat^1-profinite groups [3]. We defined the pushout cat^1-profinite groups and gave the left adjoint constructions.
Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp
Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp
Turkish Journal of Mathematics
In this paper, we present a brief review crossed modules \cite{whitehead}, cat^1-groups \cite{loday}, profinite crossed modules \cite{kortim}, cat^1-profinite groups \cite{kortim}, pullback profinite crossed modules \cite{kortim} and also the pullback cat^1- profinite groups \cite{hind}. We prove that the pulback cat^1-profinite group has a left adjoint which is the induced cat^1-group.
Some Results On Derivation Groups, Murat Alp
Some Results On Derivation Groups, Murat Alp
Turkish Journal of Mathematics
In this paper we describe a share package XMOD of functions for computing with finite, permutation crossed modules, their morphisms and derivations; cat$^1$-groups, their morphisms and their sections, written using the GAP \cite{GAP} group theory programming language. We also give some mathematical results for derivations. These results are suggested by the output produced by the XMOD package.
Left Adjoint Of Pullback Cat^1 -Groups, Murat Alp
Left Adjoint Of Pullback Cat^1 -Groups, Murat Alp
Turkish Journal of Mathematics
In [1] we define the pullback Cat^1-groups and showed that the category of pullback Cat^1-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback Cat^1-group has a left adjoint which is the induced Cat^1-group. We also give the left adjoint construction.
Pullbacks Of Crossed Modules And Cat^1-Groups, Murat Alp
Pullbacks Of Crossed Modules And Cat^1-Groups, Murat Alp
Turkish Journal of Mathematics
In this paper, wer define the pullback cat$^{1}$-groups and we showed that the category of bullback cat$^{1}$-group is equivalent to the category of pullback crossed modules. 1991 A. M. S. C.: 13D99, 16A99, 17B99, 18D35.