Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.binaryCoproductsClosure_le_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Limits.HasInitial C]
{P Q : CategoryTheory.ObjectProperty C} [Q.IsClosedUnderBinaryCoproducts]
[Q.IsClosedUnderColimitsOfShape (CategoryTheory.Discrete PEmpty.{1})], P.binaryCoproductsClosure ≤ Q ↔ P ≤ Q- Cited by
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- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, 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
- LE.le.transproof · cited by 3,151
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Limits.WalkingPairproof · cited by 1,319
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
- CategoryTheory.ObjectProperty.IsClosedUnderIsomorphismsproof · cited by 68
- CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShapestatement and proof · cited by 36
- CategoryTheory.ObjectProperty.le_colimitsClosureproof · cited by 6
- CategoryTheory.ObjectProperty.colimitsClosure_leproof · cited by 6
- CategoryTheory.ObjectProperty.IsClosedUnderBinaryCoproductsstatement and proof · cited by 5
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