Theorems · Definition · category theory

CategoryTheory.coreflectorAdjunction

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (j : CategoryTheory.Functor C D) → [inst_2 : CategoryTheory.Coreflective j] → j ⊣ CategoryTheory.coreflector j

The adjunction j ⊣ coreflector j when j is coreflective.

Defined in: Mathlib.CategoryTheory.Adjunction.Reflective
Cited by: 3 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Coreflective

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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.Coreflectivestatement and proof · cited by 9
CategoryTheory.coreflectorstatement · cited by 3
CategoryTheory.Coreflective.adjproof · cited by 0

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.essImage.counit_isIsostatement and proof · cited by 1
CategoryTheory.Functor.fullyFaithfulOfCoreflectiveproof · cited by 0
CategoryTheory.counit_obj_eq_map_counitstatement and proof · cited by 0
CategoryTheory.mem_essImage_of_counit_isSplitEpistatement and proof · cited by 0