diff --git a/Mathlib/CategoryTheory/FiberedCategory/HasFibers.lean b/Mathlib/CategoryTheory/FiberedCategory/HasFibers.lean index 5fd1b7e6fa0e7..7f4ff79513a0c 100644 --- a/Mathlib/CategoryTheory/FiberedCategory/HasFibers.lean +++ b/Mathlib/CategoryTheory/FiberedCategory/HasFibers.lean @@ -30,8 +30,7 @@ Here is an example of when this typeclass is useful. Suppose we have a presheaf `F : 𝒮ᵒᵖ ⥤ Type _`. The associated fibered category then has objects `(S, a)` where `S : 𝒮` and `a` is an element of `F(S)`. The fiber category `Fiber p S` is then equivalent to the discrete category `Fib S` with objects `a` in `F(S)`. In this case, the `HasFibers` instance is given by the -categories `F(S)` and the functor `ι` sends `a : F(S)` to `(S, a)` in the fibered category. See -`Presheaf.lean` for more details. +categories `F(S)` and the functor `ι` sends `a : F(S)` to `(S, a)` in the fibered category. ## Main API The following API is developed so that the fibers from a `HasFibers` instance can be used @@ -79,7 +78,7 @@ namespace HasFibers @[default_instance] instance canonical (p : 𝒳 ⥤ 𝒮) : HasFibers p where Fib := Fiber p - ι S := @fiberInclusion _ _ _ _ p S + ι S := fiberInclusion comp_const S := fiberInclusion_comp_eq_const equiv S := by exact isEquivalence_of_iso (F := 𝟭 (Fiber p S)) (Iso.refl _) @@ -87,7 +86,7 @@ section variable (p : 𝒳 ⥤ 𝒮) [HasFibers p] (S : 𝒮) -instance : Category (Fib p S) := isCategory S +attribute [instance] isCategory /-- The induced functor from `Fib p S` to the standard fiber. -/ @[simps!]