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Theorems · Theorem · order theory

GaloisConnection.compose

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ] {l1 : α → β}
  {u1 : β → α} {l2 : β → γ} {u2 : γ → β},
  GaloisConnection l1 u1 → GaloisConnection l2 u2 → GaloisConnection (l2 ∘ l1) (u1 ∘ u2)
Defined in
Mathlib.Order.GaloisConnection.Defs
Cited by
6 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
PreorderPreorderPreorder
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Around this declaration

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

Ideal.map_map · cited by 37Ideal.map_mapGaloisConnection.l_comm_of_u_comm · cited by 15GaloisConnection.l_comm_o…PrimeSpectrum.gc_set · cited by 7PrimeSpectrum.gc_setProjectiveSpectrum.gc_set · cited by 6ProjectiveSpectrum.gc_setIdeal.IsHomogeneous.iff_exists · cited by 2IsHomogeneous.iff_existsGaloisConnection.u_comm_of_l_comm · cited by 2GaloisConnection.u_comm_o…Preorder · cited by 7952PreorderGaloisConnection · cited by 253GaloisConnectionGaloisConnection.composeCITED BYCITES

Cites2

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Cited by6

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