Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iff_op
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.ObjectProperty C) (J : Type u')
[inst_1 : CategoryTheory.Category.{v', u'} J], P.IsClosedUnderColimitsOfShape J ↔ P.op.IsClosedUnderLimitsOfShape Jᵒᵖ- 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.
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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShapestatement and proof · cited by 49
- CategoryTheory.ObjectProperty.opstatement and proof · cited by 42
- CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShapestatement · cited by 36
- CategoryTheory.ObjectProperty.colimitsOfShapeproof · cited by 35
- CategoryTheory.ObjectProperty.limitsOfShapeproof · cited by 26
- CategoryTheory.ObjectProperty.op_unopproof · cited by 10
- CategoryTheory.ObjectProperty.op_monotone_iffproof · cited by 6
- CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_iffproof · cited by 4
- CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_op_iff_unopproof · cited by 0