A. M. S. Classification: 18G30, 18G55.

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....

conclusions the patient underwent surgery applying a midline incision. the left kidney showed a lump pattern embedded in lower pole of the right kidney. left sided nephrectomy was performed while temporary right renal artery was clamped temporarily. histopathological evaluation revealed clear cell carcinoma with severe nuclear atypia (fuhrman grade 4/4). however, local recurrence was not detect...