Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.Embedding.toHom

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

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

Defined in
Mathlib.ModelTheory.Basic
Cited by
40 results in Mathlib
Foundations
Depth 16 from the axioms · uses 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.Embedding.equivRange · cited by 14Embedding.equivRangeFirstOrder.Language.Substructure.fg_iff_structure_fg · cited by 12Substructure.fg_iff_struc…FirstOrder.Language.Embedding.toPartialEquiv · cited by 6Embedding.toPartialEquivFirstOrder.Language.Embedding.codRestrict · cited by 6Embedding.codRestrictFirstOrder.Language.Embedding.coe_toHom · cited by 4Embedding.coe_toHomFirstOrder.Language.Substructure.range_subtype · cited by 3Substructure.range_subtypeFirstOrder.Language.Embedding.substructureEquivMap · cited by 2Embedding.substructureEqu…FirstOrder.Language.Embedding.subtype_equivRange · cited by 2Embedding.subtype_equivRa…FirstOrder.Language.Embedding.toHom_injective · cited by 2Embedding.toHom_injectiveFirstOrder.Language.Hom.domRestrict · cited by 2Hom.domRestrictFirstOrder.Language.age.countable_quotient · cited by 2age.countable_quotientFirstOrder.Language.age.jointEmbedding · cited by 2age.jointEmbeddingFirstOrder.Language.IsUltrahomogeneous.extend_embedding · cited by 2IsUltrahomogeneous.extend…FirstOrder.Language.PartialEquiv.domRestrict · cited by 2PartialEquiv.domRestrictFirstOrder.Language.Embedding.toHom_comp_injective · cited by 1Embedding.toHom_comp_inje…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Embedding · cited by 128Language.EmbeddingFirstOrder.Language.Hom · cited by 107Language.HomFirstOrder.Language.HomClass.toHom · cited by 1HomClass.toHomEmbedding.toHomCITED BYCITES

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Cited by46

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