Title of article :
Crossed squares, crossed modules over groupoids and cat1−2−groupoids
Author/Authors :
Temel, Sedat Department of Mathematics - Faculty of Arts and Science - Recep Tayyip Erdogan University, Rize, Turkey
Abstract :
The aim of this paper is to introduce the notion of cat1−groupoids which are the groupoid version of cat1−groups and to prove the categorical equivalence between crossed modules over groupoids and cat1−groupoids. In section 4 we introduce the notions of crossed squares over groupoids and of cat2−groupoids, and then we show their categories are equivalent. These equivalences enable us to obtain more examples of groupoids
Keywords :
Crossed module , crossed square , groupoid , catbf1−group , catbf2−group
Journal title :
Categories and General Algebraic Structures with Applications
