Homotopy Type Theory set > history (Rev #7, changes)

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A set consists of

  • A type AA
  • A 0-truncator
    τ 0: (a:A) (b:A)isProp(a=b)\tau_0: \prod_{(a:A)} \prod_{(b:A)} \mathrm{isProp}(a = b)

As univalent setoids

A set is a setoid TT where the canonical functions

a:T,b:Tidtoiso(a,b):(a= Tb)(ab)a:T, b:T \vdash idtoiso(a,b):(a =_T b) \to (a \equiv b)

are equivalences

p: a:A b:A(a= Tb)(ab)p: \prod_{a:A} \prod_{b:A} (a =_T b) \cong (a \equiv b)


See also


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