Theorems · Theorem · category theory

CategoryTheory.Adjunction.hasColimit_comp_equivalence

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type u} [inst_2 : CategoryTheory.Category.{v, u} J] (K : CategoryTheory.Functor J C)
  (E : CategoryTheory.Functor C D) [E.IsEquivalence] [CategoryTheory.Limits.HasColimit K],
  CategoryTheory.Limits.HasColimit (K.comp E)

Defined in: Mathlib.CategoryTheory.Adjunction.Limits
Cited by: 1 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsEquivalence CategoryTheory.Limits.HasColimit

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Limits.HasColimitstatement and proof · cited by 307
CategoryTheory.Limits.colimit.isColimitproof · cited by 193
CategoryTheory.Functor.mapCoconeproof · cited by 161
CategoryTheory.Limits.colimit.coconeproof · cited by 136
CategoryTheory.Limits.isColimitOfPreservesproof · cited by 118
CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
CategoryTheory.Limits.HasColimit.mkproof · cited by 25

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Adjunction.hasColimit_of_comp_equivalenceproof · cited by 1