Theorems · Definition · category theory
CategoryTheory.MorphismProperty.underObj
{T : Type u_3} →
[inst : CategoryTheory.Category.{v_3, u_3} T] →
CategoryTheory.MorphismProperty T → {X : T} → CategoryTheory.ObjectProperty (CategoryTheory.Under X)The object property on Under X induced by a morphism property.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.ObjectPropertystatement · cited by 798
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.Under.rightproof · cited by 128
- CategoryTheory.Under.homproof · cited by 73
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.underObj_iffstatement · cited by 2
- CategoryTheory.MorphismProperty.ind_iff_existsproof · cited by 1
- CategoryTheory.MorphismProperty.ind_iff_ind_underMkstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.underObj_ind_eq_ind_underObjstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.inverseImage_op_overObjstatement · cited by 0
- CategoryTheory.MorphismProperty.inverseImage_op_underObjstatement · cited by 0
- CategoryTheory.MorphismProperty.ind_indproof · cited by 0
- CategoryTheory.MorphismProperty.ind_underObj_pushoutstatement and proof · cited by 0
- RingHom.HasEqualizers.isClosedUnderLimitsOfShapestatement and proof · cited by 0
- RingHom.HasFiniteProducts.isClosedUnderLimitsOfShapestatement and proof · cited by 0