Theorems · Theorem · category theory
CategoryTheory.Adjunction.isLocalization
∀ {C₁ : Type u_1} {C₂ : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
[inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] {G : CategoryTheory.Functor C₁ C₂} {F : CategoryTheory.Functor C₂ C₁}
(adj : G ⊣ F) [F.Full] [F.Faithful],
G.IsLocalization ((CategoryTheory.MorphismProperty.isomorphisms C₂).inverseImage G)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.MorphismPropertyproof · cited by 2,179
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Equivalenceproof · cited by 601
- CategoryTheory.Iso.transproof · cited by 566
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.isLocalization'proof · cited by 1
- CategoryTheory.ObjectProperty.isLocalization_isLocalproof · cited by 0
- CategoryTheory.Abelian.isLocalization_isoModSerre_kernel_of_leftAdjointproof · cited by 0