Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiber_map_fiberMk

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C]
  {N : Type u'} [inst_2 : CategoryTheory.Category.{v', u'} N] (p : CategoryTheory.Functor N C)
  [inst_3 : CategoryTheory.InitiallySmall N] {U : N} {X : C} (f : p.obj U ⟶ X) {Y : C} (g : X ⟶ Y),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiber p).map g))
      (CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk f) =
    CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk (CategoryTheory.CategoryStruct.comp f g)

Defined in

Mathlib.CategoryTheory.Sites.Point.OfIsCofiltered

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.CategoryCategoryTheory.InitiallySmall