Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.Equiv.toHom

{L : FirstOrder.Language} →
  {M : Type w} → {N : Type w'} → [inst : L.Structure M] → [inst_1 : L.Structure N] → L.Equiv M N → L.Hom M N

A first-order equivalence is also a first-order homomorphism.

Defined in
Mathlib.ModelTheory.Basic
Cited by
11 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.Equiv.fg_iff · cited by 3Equiv.fg_iffFirstOrder.Language.Equiv.refl_toHom · cited by 2Equiv.refl_toHomFirstOrder.Language.Equiv.comp_toHom · cited by 2Equiv.comp_toHomFirstOrder.Language.IsUltrahomogeneous.amalgamation_age · cited by 1IsUltrahomogeneous.amalga…FirstOrder.Language.Equiv.coe_toHom · cited by 0Equiv.coe_toHomFirstOrder.Language.Equiv.self_comp_symm_toHom · cited by 0Equiv.self_comp_symm_toHomFirstOrder.Language.countable_self_fgequiv_of_countable · cited by 0Language.countable_self_f…FirstOrder.Language.Equiv.symm_comp_self_toHom · cited by 0Equiv.symm_comp_self_toHomFirstOrder.Language.Equiv.toEmbedding_toHom · cited by 0Equiv.toEmbedding_toHomFirstOrder.Language.Equiv.toHom_range · cited by 0Equiv.toHom_rangeFirstOrder.Language.Equiv.cg_iff · cited by 0Equiv.cg_iffFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Hom · cited by 107Language.HomFirstOrder.Language.Equiv · cited by 83Language.EquivFirstOrder.Language.HomClass.toHom · cited by 1HomClass.toHomEquiv.toHomCITED BYCITES

Cites5

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Cited by11

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