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Theorems · Definition · category theory

CategoryTheory.reflector

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (i : CategoryTheory.Functor D C) → [CategoryTheory.Reflective i] → CategoryTheory.Functor C D

The reflector C ⥤ D when R : D ⥤ C is reflective.

Defined in
Mathlib.CategoryTheory.Adjunction.Reflective
Cited by
17 results in Mathlib
Foundations
Depth 4 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.reflectorAdjunction · cited by 10CategoryTheory.reflectorA…CategoryTheory.unitCompPartialBijective · cited by 6CategoryTheory.unitCompPa…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_natural · cited by 1CategoryTheory.unitCompPa…CategoryTheory.unitCompPartialBijective_symm_natural · cited by 1CategoryTheory.unitCompPa…CategoryTheory.preservesBinaryProducts_of_exponentialIdeal · cited by 1CategoryTheory.preservesB…CategoryTheory.equivEssImageOfReflective_counitIso · cited by 0CategoryTheory.equivEssIm…CategoryTheory.equivEssImageOfReflective_inverse · cited by 0CategoryTheory.equivEssIm…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Reflective · cited by 27CategoryTheory.ReflectiveCategoryTheory.Reflective.L · cited by 0Reflective.LCategoryTheory.reflectorCITED BYCITES

Cites4

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Cited by25

Results whose statement or proof uses this declaration.