%0 Journal Article
%T Crossed squares, crossed modules over groupoids and cat$^{\bf {1-2}}-$groupoids
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Temel, Sedat
%D 2020
%\ 07/01/2020
%V 13
%N 1
%P 125-142
%! Crossed squares, crossed modules over groupoids and cat$^{\bf {1-2}}-$groupoids
%K crossed module
%K crossed square
%K groupoid
%K cat$^{bf {1}}-$group
%K cat$^{bf {2}}-$group
%R 10.29252/cgasa.13.1.125
%X 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. In section 4 we introduce the notions of crossed squares over groupoids and of cat$^{\bf {2}}-$groupoids, and then we show their categories are equivalent. These equivalences enable us to obtain more examples of groupoids.
%U https://cgasa.sbu.ac.ir/article_87511_b595acc78c30c8580458ad2fc0331d2f.pdf