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  • MODELS OF MARTIN-LÖF TYPE THEORY FROM ALGEBRAIC WEAK FACTORISATION SYSTEMS

  • Part of
  • NICOLA GAMBINO, MARCO FEDERICO LARREA
  • Journal:
    The Journal of Symbolic Logic / Volume 88 / Issue 1 / March 2023
    Published online by Cambridge University Press:
    08 June 2021, pp. 242-289
    Print publication:
    March 2023
    • Article
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  • We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-Löf type theory. This is done by showing that the comprehension category associated with a type-theoretic algebraic weak factorisation system satisfies the assumptions necessary to apply a right adjoint method for splitting comprehension categories. We then provide methods for constructing several examples of type-theoretic algebraic weak factorisation systems, encompassing the existing groupoid and cubical sets models, as well as new models based on normal fibrations.