Theorems · Theorem · category theory
CategoryTheory.Adjunction.isContinuous_of_isCocontinuous
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] (J : CategoryTheory.GrothendieckTopology C)
(K : CategoryTheory.GrothendieckTopology D) {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
(adj : F ⊣ G) [F.IsCocontinuous J K], G.IsContinuous K J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Adjunctionstatement and proof · cited by 524
- CategoryTheory.Functor.IsContinuousstatement · cited by 100
- CategoryTheory.Functor.IsCocontinuousstatement and proof · cited by 55
- CategoryTheory.Functor.IsRightAdjointproof · cited by 46
- CategoryTheory.Adjunction.isRightAdjointproof · cited by 8
- CategoryTheory.Functor.isContinuous_of_coverPreservingproof · cited by 4
- CategoryTheory.compatiblePreservingOfFlatproof · cited by 3
- CategoryTheory.Adjunction.isCocontinuous_iff_coverPreservingproof · cited by 2
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