Theorems · Inductive type · category theory
CategoryTheory.IsReflexivePair
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {A B : C} → (A ⟶ B) → (A ⟶ B) → PropThe pair f g : A ⟶ B is reflexive if there is a morphism B ⟶ A which is a section for both.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
Cited by29
Results whose statement or proof uses this declaration.
- CategoryTheory.commonSectionstatement and proof · cited by 7
- CategoryTheory.Limits.ofIsReflexivePairstatement and proof · cited by 6
- CategoryTheory.Limits.colimitOfIsReflexivePairIsoCoequalizerstatement and proof · cited by 4
- CategoryTheory.section_comp_leftstatement and proof · cited by 3
- CategoryTheory.section_comp_rightstatement and proof · cited by 3
- CategoryTheory.IsReflexivePair.mk'statement · cited by 3
- CategoryTheory.IsReflexivePair.common_sectionstatement and proof · cited by 2
- CategoryTheory.Limits.ι_colimitOfIsReflexivePairIsoCoequalizer_homstatement and proof · cited by 1
- CategoryTheory.Limits.π_colimitOfIsReflexivePairIsoCoequalizer_invstatement and proof · cited by 1
- CategoryTheory.IsReflexivePair.common_section'statement and proof · cited by 1
- CategoryTheory.section_comp_left_assocstatement and proof · cited by 0
- CategoryTheory.section_comp_right_assocstatement and proof · cited by 0