Geodesic
Homotopies in Grothendieck fibrations
Theory and applications of categories, Tome 35 (2020), pp. 1312-1378 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category C, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories C/A, and we show that in the case C=Top, our construction applied to this fibration recovers the usual 2-category of spaces.

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Classification : Primary: 18D30. Secondary: 55U35
Keywords: Grothendieck fibrations, hyperdoctrine, 2-category 
@article{TAC_2020_35_a34,
     author = {Joseph Helfer},
     title = {Homotopies in {Grothendieck} fibrations},
     journal = {Theory and applications of categories},
     pages = {1312--1378},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a34/}
}
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Joseph Helfer. Homotopies in Grothendieck fibrations. Theory and applications of categories, Tome 35 (2020), pp. 1312-1378. http://geodesic.mathdoc.fr/item/TAC_2020_35_a34/