Equivalence between pseudofunctors C → Cat and Grothendieck fibrations over C. The total category ∫F has objects (c, x) with x ∈ F(c) and morphisms (c,x) → (c',x') consisting of f: c → c' plus φ: F(f)(x) → x'. Foundation of indexed…
Equivalence between pseudofunctors C → Cat and Grothendieck fibrations over C. The total category ∫F has objects (c, x) with x ∈ F(c) and morphisms (c,x) → (c',x') consisting of f: c → c' plus φ: F(f)(x) → x'. Foundation of indexed…