On the Symmetric Crossed Polymodule on a Category of Polymodules
Subject Areas : International Journal of Industrial Mathematics
Mohammad Ali Dehghanizadeh
1
,
Saeed Mirvakili
2
1 - Department of Mathematics, Technical and Vocational University (TVU); Tehran, Iran
2 - Department of Mathematics,
Payame Noor University,
Tehran, Iran
Keywords: Group, Polygroup, Crossed module&lrm, , &lrm, Crossed polymodule&lrm, , &lrm, Symmetric&lrm, crossed polymodule,
Abstract :
The theory of polygroups is a natural extension of group theory, where the composition of two elements results in a set rather than an element. This concept has found applications in diverse fields such as geometry, lattices, combinatorics, and color schemes. Addition- ally, the study of crossed modules and their applications has played a crucial role in category theory, homology and cohomology of groups, homotopy theory, algebra, k-theory, and more. This paper presents the definition of a polyfunctor and transformation for polygroups, as well as the introduction of the concept of symmetric crossed module to sym- metric crossed polymodules. Our findings extend the classical results of crossed modules to crossed polymodules of polygroups.