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What's the correct term for it?

  1. Sep 26, 2006 #1

    zef

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    How do we call such relation between mappings f:A->A and g:B->B when there exists one-to-one mapping h:A->B such that for any a from A f(a)=g(h(a))?

    Example.

    f: {T, F) -> {T, F}
    where f(x) = not x

    g : {0, 1} -> {0, 1}
    where f(x)=1-x

    h: {T, F} -> {0, 1}
    where h(T)=1, h(F)=0
     
  2. jcsd
  3. Sep 26, 2006 #2
    Hmm, technically f(a) cannot be equal to g(h(a)) unless codomain(f) = codomain(g).
     
  4. Sep 26, 2006 #3

    HallsofIvy

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    You just said f:A->A and g:B->B. For any function h:A->B, g(h(x)) is in B, not A.
     
  5. Sep 26, 2006 #4

    zef

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    Sorry, it should be h(f(a))=g(h(a))
     
  6. Sep 26, 2006 #5

    HallsofIvy

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    Science Advisor

    I don't know any specific name for the function h, but what you have is a "commutative diagram" used in Algebraic Topology and Category Theory.
     
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