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math.LO2024
A Foundation for Synthetic Stone Duality
Felix Cherubini, Thierry Coquand, Freek Geerligs +1
The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski…
math.AT2024
The equivariant model structure on cartesian cubical sets
Steve Awodey, Evan Cavallo, Thierry Coquand +2
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves…
math.AG2024
Projective Space in Synthetic Algebraic Geometry
Felix Cherubini, Thierry Coquand, Matthias Ritter +1
Synthetic algebraic geometry is a new approach to algebraic geometry. It consists in using homotopy type theory extended with three axioms, together with the interpretation of thes…