Crossed squares, crossed modules over groupoids and cat$^{\bf {1-2}}-$groupoids | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 8، دوره 13، شماره 1، مهر 2020، صفحه 125-142 اصل مقاله (528.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.13.1.125 | ||
| نویسنده | ||
| Sedat Temel | ||
| Department of Mathematics, Faculty of Arts and Science, Recep Tayyip Erdogan University, Rize, Turkey. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Crossed module؛ crossed square؛ groupoid؛ cat$^{bf {1}}-$group؛ cat$^{bf {2}}-$group | ||
| مراجع | ||
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