Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsClosedUnderBinaryProducts.closedUnderIsomorphisms
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.ObjectProperty C)
[CategoryTheory.Limits.HasTerminal C] [P.IsClosedUnderLimitsOfShape (CategoryTheory.Discrete PEmpty.{1})]
[P.IsClosedUnderBinaryProducts], P.IsClosedUnderIsomorphisms- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.IsLimitproof · cited by 664
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.binaryProductsClosure_le_iffproof · cited by 1
- CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts.mk'proof · cited by 0