Cartesian fibration

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Published on July 7, 2025 12:00:00 AM ● Video Link: https://www.youtube.com/watch?v=PT2QKbD9YZo

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In mathematics, especially homotopy theory, a cartesian fibration is, roughly, a map so that every lift exists that is a final object among all lifts. For example, the forgetful functor
QCoh → Sch from the category of pairs (X, F) of schemes and quasi-coherent sheaves on them is a cartesian fibration (see). In fact, the Grothendieck construction says all cartesian fibrations are of this type; i.e., they simply forget extra data. See also: fibred category, prestack.
The dual of a cartesian fibration is called an op-fibration; in particular, not a cocartesian fibration.
A right fibration between simplicial sets is an example of a cartesian fibration.

Source: https://en.wikipedia.org/wiki/Cartesian_fibration
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