Geodesic
Stacks and sheaves of categories as fibrant objects, I
Theory and applications of categories, Tome 29 (2014), pp. 654-695.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We show that the category of categories fibred over a site is a generalized Quillen model category in which the weak equivalences are the local equivalences and the fibrant objects are the stacks, as they were defined by J. Giraud. The generalized model category restricts to one on the full subcategory whose objects are the categories fibred in groupoids. We show that the category of sheaves of categories is a model category that is Quillen equivalent to the generalized model category for stacks and to the model category for strong stacks due to A. Joyal and M. Tierney.
Publié le :
Classification : 18G55, 18D30, 14A20
Keywords: fibred category, model category, stack 
@article{TAC_2014_29_a23,
     author = {Alexandru E. Stanculescu},
     title = {Stacks and sheaves of categories as fibrant objects, {I}},
     journal = {Theory and applications of categories},
     pages = {654--695},
     publisher = {mathdoc},
     volume = {29},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a23/}
}
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Alexandru E. Stanculescu. Stacks and sheaves of categories as fibrant objects, I. Theory and applications of categories, Tome 29 (2014), pp. 654-695. http://geodesic.mathdoc.fr/item/TAC_2014_29_a23/