Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.limitsOfShape_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.op.limitsOfShape J = (P.colimitsOfShape Jᵒᵖ).op- Cited by
- 1 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.opstatement and proof · cited by 42
- CategoryTheory.ObjectProperty.colimitsOfShapestatement · cited by 35
- CategoryTheory.opOpEquivalenceproof · cited by 34
- CategoryTheory.ObjectProperty.limitsOfShapestatement and proof · cited by 26
- CategoryTheory.ObjectProperty.op_unopproof · cited by 10
- CategoryTheory.ObjectProperty.limitsOfShape_congrproof · cited by 2
- CategoryTheory.ObjectProperty.colimitsOfShape_eq_unop_limitsOfShapeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_opproof · cited by 1