Homotopy Type Theory
نویسنده
چکیده
Introduction 3 1 A short guide to constructive type theory 7 1.1 A dependent type over a type . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Dependent products . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.2 Dependent sums . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Defining types inductively . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Type theory with identity types 14 2.1 The inductive definition of identity types . . . . . . . . . . . . . . . . . . 15 2.2 More properties of paths . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 Preservation of composition . . . . . . . . . . . . . . . . . . . . 21 2.2.2 Preservation of inversion . . . . . . . . . . . . . . . . . . . . . . 23 2.2.3 The dependent type Y(a) . . . . . . . . . . . . . . . . . . . . . . 23
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