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Indexed Grothendieck construction
Elena Caviglia, Luca Mesiti
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 a…
Colimits in 2-dimensional slices
Luca Mesiti
We generalize to dimension 2 the well-known fact that a colimit in a 1-dimensional slice is precisely the map from the colimit of the domains of the diagram that is induced by the…
A comonad for Grothendieck fibrations
Jacopo Emmenegger, Luca Mesiti, Giuseppe Rosolini +1
We prove that cloven Grothendieck fibrations over a fixed base $\ct{B}$ are the pseudo-coalgebras for a lax idempotent 2-comonad on $\ct{Cat}/\ct{B}$. We show this via an original…
Pointwise Kan extensions along 2-fibrations and the 2-category of elements
Luca Mesiti
We study the 2-category of elements from an abstract point of view. We generalize to dimension 2 the well-known result that the category of elements can be captured by a comma obje…