Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk_map_comp

∀ {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 V : N} (g : V ⟶ U) {X : C} (f : p.obj U ⟶ X),
  CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk (CategoryTheory.CategoryStruct.comp (p.map g) f) =
    CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk f

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