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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 ⊣ i

The adjunction reflector i ⊣ i when i is reflective.

Defined in
Mathlib.CategoryTheory.Adjunction.Reflective
Cited by
10 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Reflective

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.equivEssImageOfReflective · cited by 4CategoryTheory.equivEssIm…CategoryTheory.bijection · cited by 3CategoryTheory.bijectionCategoryTheory.unitCompPartialBijectiveAux · cited by 2CategoryTheory.unitCompPa…CategoryTheory.unitCompPartialBijective_symm_apply · cited by 2CategoryTheory.unitCompPa…CategoryTheory.Functor.essImage.unit_isIso · cited by 2essImage.unit_isIsoCategoryTheory.unitCompPartialBijectiveAux_symm_apply · cited by 1CategoryTheory.unitCompPa…CategoryTheory.bijection_natural · cited by 1CategoryTheory.bijection_…CategoryTheory.bijection_symm_apply_id · cited by 1CategoryTheory.bijection_…CategoryTheory.unitCompPartialBijective_symm_natural · cited by 1CategoryTheory.unitCompPa…CategoryTheory.Functor.fullyFaithfulOfReflective · cited by 1Functor.fullyFaithfulOfRe…CategoryTheory.equivEssImageOfReflective_counitIso · cited by 0CategoryTheory.equivEssIm…CategoryTheory.equivEssImageOfReflective_unitIso · cited by 0CategoryTheory.equivEssIm…CategoryTheory.unit_obj_eq_map_unit · cited by 0CategoryTheory.unit_obj_e…CategoryTheory.exponentialIdealReflective · cited by 0CategoryTheory.exponentia…CategoryTheory.CartesianMonoidalCategory.ofReflective · cited by 0CartesianMonoidalCategory…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Adjunction · cited by 524CategoryTheory.AdjunctionCategoryTheory.Reflective · cited by 27CategoryTheory.ReflectiveCategoryTheory.reflector · cited by 17CategoryTheory.reflectorCategoryTheory.Reflective.adj · cited by 0Reflective.adjCategoryTheory.reflectorAdjun…CITED BYCITES

Cites6

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Cited by17

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