Identity in homotopy type theory, part I: The justification of path induction

James Ladyman, Stuart Presnell

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)


Homotopy Type Theory (HoTT) is a proposed new language and foundation for mathematics, combining algebraic topology with logic. An important rule for the treatment of identity in HoTT is path induction, which is commonly explained by appeal to the homotopy interpretation of the theory's types, tokens, and identities as (respectively) spaces, points, and paths. However, if HoTT is to be an autonomous foundation then such an interpretation cannot play a fundamental role. In this paper we give a derivation of path induction, motivated from pre-mathematical considerations, without recourse to homotopy theory.

Original languageEnglish
Article numbernkv014
Pages (from-to)386-406
Number of pages21
JournalPhilosophia Mathematica
Issue number3
Publication statusPublished - 1 Oct 2015

Structured keywords

  • Centre for Science and Philosophy
  • Centre_for_science_and_philosophy


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