Category Theory For Beginners: Fibrations and Lenses

We introduce fibrations intuitively by starting with discrete op fibrations. We describe connections and applications involving the category of elements, and then generalize to get to Grothendieck constructions and op fibrations. Then we dualize to obtain descriptions of contravariant Grothendieck constructions and fibrations. Then we illustrate applications of fibrations to logic, indexed sets, lenses and dynamical systems. We also connect with Kan extensions.
Resources:
Unlisted video on factorizing a functor
• Factorizing a functor
Categorical Logic and Type Theory
Bart Jacobs
people.mpi-sws...
Coend calculus
Fosco Loregian
arxiv.org/abs/...
Generalized Lens Categories via functors Cop→Cat
David I. Spivak
arxiv.org/abs/...
Framed bicategories and monoidal fibrations
Michael A. Shulman
arxiv.org/abs/...
In this folder I have a handwritten proof that the projection functor associated with the covariant Grothendieck construction is an opfibration.
drive.google.c...
In this folder one can find a sketch describing how to go from an opfibration to the corresponding Grothendieck construction
drive.google.c...
This folder has more interesting ideas
drive.google.c...