Dualizing cartesian and cocartesian fibrations
By Clark Barwick, Saul Glasman, Denis Nardin. Theory and Applications of Categories, 2014
64 citations recorded by the source corpus.
In this technical note, we proffer a very explicit construction of the "dual cocartesian fibration" $p^{\vee}$ of a cartesian fibration $p$, and we show they are classified by the same functor to $\mathbf{Cat}_{\infty}$.
Subfields: Algebra and Number Theory
View Paper: https://www.semanticscholar.org/paper/f2cca9db1f2603332fcee0718cfa0b604faa4450
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In Algebra and Number Theory
Citations in the corpus
- Lax monoidal adjunctions, two‐variable fibrations and the calculus of mates (2020, methodology): “(3) By restricting to one of the two legs in the previous point, the dualisation of bifibrations is also discussed in detail in [HLAS16, Section 5], [HMS20, Section A.1] and [CDH+23, Section 7.1] (4) In [HHLN21] we also supply a more explicit description of the equivalences in Theorem 2.5.1 based on”
- Lax colimits and free fibrations in ∞-categories (2017, methodology): “The twisted arrow ∞ -category, which was originally introduced by Joyal, has previously been extensively used by Barwick [Bar13,Bar17] and collaborators [BGN14], and by Lurie [ A natural definition of (co)ends in the ∞ -categorical setting is then the following.”