Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.eq_inverseImage_quotientFunctor
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (W : CategoryTheory.MorphismProperty C)
(homRel : HomRel C) [inst_1 : CategoryTheory.HomRel.IsStableUnderPrecomp homRel]
[inst_2 : CategoryTheory.HomRel.IsStableUnderPostcomp homRel] [inst_3 : W.HasQuotient homRel],
W = (W.quotient homRel).inverseImage (CategoryTheory.Quotient.functor homRel)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
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Cites13
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.inverseImagestatement and proof · cited by 83
- CategoryTheory.MorphismProperty.extproof · cited by 61
- HomRelstatement and proof · cited by 49
- CategoryTheory.Quotientstatement · cited by 48
- CategoryTheory.Quotient.functorstatement and proof · cited by 41
- CategoryTheory.HomRel.IsStableUnderPostcompstatement and proof · cited by 7
- CategoryTheory.HomRel.IsStableUnderPrecompstatement and proof · cited by 7
- CategoryTheory.MorphismProperty.HasQuotientstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.quotient_iffproof · cited by 3
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