Geodesic
Indexed Grothendieck construction
Theory and applications of categories, Tome 41 (2024), pp. 894-926 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We produce an indexed version of the Grothendieck construction. This gives an equivalence of categories between opfibrations over a fixed base in the 2-category of 2-copresheaves and 2-copresheaves on the Grothendieck construction of the fixed base. We also prove that this equivalence is pseudonatural in the base and that it restricts to discrete opfibrations with small fibres and copresheaves. Our result is a 2-dimensional generalization of the equivalence between slices of copresheaves and copresheaves on slices. We can think of the indexed Grothendieck construction as a simultaneous Grothendieck construction on every index that takes into account all bonds between different indexes.

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Classification : 18D30, 18N10, 18F20, 18B25, 18A30
Keywords: Grothendieck construction, indexed, category of elements, fibration, presheaf, 2-category 
@article{TAC_2024_41_a27,
     author = {Elena Caviglia and Luca Mesiti},
     title = {Indexed {Grothendieck} construction},
     journal = {Theory and applications of categories},
     pages = {894--926},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a27/}
}
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Elena Caviglia; Luca Mesiti. Indexed Grothendieck construction. Theory and applications of categories, Tome 41 (2024), pp. 894-926. http://geodesic.mathdoc.fr/item/TAC_2024_41_a27/