Algebraic Type Theory, Part 1: Martin-L\"of algebras

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Steve Awodey This is my paper · ORCID

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keywords theoryalgebraictypealgebrasdependentderivedideasmartin-l

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A new algebraic treatment of dependent type theory is proposed using ideas derived from topos theory and algebraic set theory.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Internal Algebraic Type Theory
math.CT 2026-07 conditional novelty 7.0 of 10

Maps that are exponentiable with respect to a family of maps give polynomial functors and an algebraic model of directed type theory in the category of categories with hom-types.
Bidirectional Elaborators \`a la Carte
cs.PL 2026-07 accept novelty 7.0 of 10

A monadic DSL yields correct-by-construction, substitution-stable bidirectional elaborators for Martin-Löf type theory that extract algebraically from a presheaf model.