Theorems · Theorem · category theory
CategoryTheory.CostructuredArrow.isSeparating_inverseImage_proj
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(S : CategoryTheory.Functor C D) (T : D) {P : CategoryTheory.ObjectProperty C},
P.IsSeparating → (P.inverseImage (CategoryTheory.CostructuredArrow.proj S T)).IsSeparating- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Comma.leftproof · cited by 886
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.CostructuredArrowstatement and proof · cited by 536
- CategoryTheory.CommaMorphism.leftproof · cited by 526
- CategoryTheory.CostructuredArrow.homproof · cited by 179
- CategoryTheory.CostructuredArrow.mkproof · cited by 155
- CategoryTheory.CostructuredArrow.projstatement and proof · cited by 122
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.isLeftAdjoint_of_preservesColimits_of_isSeparatingproof · cited by 1