Theorems · Definition · category theory
CategoryTheory.reflectorAdjunction
{C : Type u₁} →
{D : Type u₂} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(i : CategoryTheory.Functor D C) → [inst_2 : CategoryTheory.Reflective i] → CategoryTheory.reflector i ⊣ iThe adjunction reflector i ⊣ i when i is reflective.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Adjunctionstatement · cited by 524
- CategoryTheory.Reflectivestatement and proof · cited by 27
- CategoryTheory.reflectorstatement · cited by 17
- CategoryTheory.Reflective.adjproof · cited by 0
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.equivEssImageOfReflectiveproof · cited by 4
- CategoryTheory.bijectionproof · cited by 3
- CategoryTheory.unitCompPartialBijectiveAuxproof · cited by 2
- CategoryTheory.unitCompPartialBijective_symm_applystatement and proof · cited by 2
- CategoryTheory.Functor.essImage.unit_isIsostatement and proof · cited by 2
- CategoryTheory.unitCompPartialBijectiveAux_symm_applystatement and proof · cited by 1
- CategoryTheory.bijection_naturalproof · cited by 1
- CategoryTheory.bijection_symm_apply_idproof · cited by 1
- CategoryTheory.unitCompPartialBijective_symm_naturalproof · cited by 1
- CategoryTheory.Functor.fullyFaithfulOfReflectiveproof · cited by 1
- CategoryTheory.equivEssImageOfReflective_counitIsostatement · cited by 0
- CategoryTheory.equivEssImageOfReflective_unitIsostatement · cited by 0