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Homomorphism indistinguishability is preserved under categorical products

Lax871432.ProductPreservation · concepts/Lax871432/ProductPreservation.lean · lax-871432

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    Natural Language Statement

    Lemma

    For every graph class F\mathcal{F}, the relaxation ≡F\equiv_{\mathcal{F}} is preserved under categorical products: if G≡FHG \equiv_{\mathcal{F}} H then G×K≡FH×KG \times K \equiv_{\mathcal{F}} H \times K for every graph KK.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    In the paper

    • page 4 of this submission's paper

    Lean source view on GitHub

    1import Lax871432.HomomorphismIndistinguishability
    2import Lax871432.PreservationProperties
    3
    4/-!
    5---
    6title: Homomorphism indistinguishability is preserved under categorical products
    7type: lemma
    8---
    9For every graph class F\mathcal{F}, the relaxation ≡F\equiv_{\mathcal{F}} is preserved under
    10categorical products: if G≡FHG \equiv_{\mathcal{F}} H then
    11G×K≡FH×KG \times K \equiv_{\mathcal{F}} H \times K for every graph KK.
    12-/
    13
    14open Lax871432.GraphClasses
    15open Lax871432.HomomorphismIndistinguishability Lax871432.PreservationProperties
    16
    17namespace Lax871432.ProductPreservation
    18
    19/-- Homomorphism indistinguishability over any graph class is preserved under categorical
    20products. -/
    21axiom preservedUnderCatProd (𝓕 : GraphClass) :
    22 PreservedUnderCatProd (homIndRel 𝓕)
    23
    24end Lax871432.ProductPreservation
    25
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