Theorems · Theorem · category theory
CategoryTheory.Limits.hasLimit_of_hasColimit_op
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} J]
(F : CategoryTheory.Functor J C) [CategoryTheory.Limits.HasColimit F.op], CategoryTheory.Limits.HasLimit F- Defined in
- Mathlib.CategoryTheory.Limits.Opposites
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.opstatement and proof · cited by 997
- CategoryTheory.Limits.HasColimitstatement and proof · cited by 307
- CategoryTheory.Limits.HasLimitstatement · cited by 226
- CategoryTheory.Limits.colimit.isColimitproof · cited by 193
- CategoryTheory.Limits.colimit.coconeproof · cited by 136
- CategoryTheory.Limits.HasLimit.mkproof · cited by 29
- CategoryTheory.Limits.Cocone.unopproof · cited by 6
- CategoryTheory.Limits.IsColimit.unopproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.hasLimitsOfShape_of_hasColimitsOfShape_opproof · cited by 6
- CategoryTheory.Limits.hasColimit_op_iff_hasLimitproof · cited by 1