Theorems · Theorem · category theory
CategoryTheory.IsKernelPair.isReflexivePair
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A B R : C} {f g : R ⟶ A} {q : A ⟶ B},
CategoryTheory.IsKernelPair q f g → CategoryTheory.IsReflexivePair f gIf f,g is a kernel pair for some morphism q, then it is reflexive.
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- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites7
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.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.IsKernelPairstatement and proof · cited by 24
- CategoryTheory.IsReflexivePairstatement · cited by 19
- CategoryTheory.IsReflexivePair.mk'proof · cited by 3
- CategoryTheory.IsKernelPair.lift'proof · cited by 1
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