# Brouwer's fixed-point theorem in real-cohesive homotopy type theory

@article{Shulman2018BrouwersFT,
title={Brouwer's fixed-point theorem in real-cohesive homotopy type theory},
author={M. Shulman},
journal={Math. Struct. Comput. Sci.},
year={2018},
volume={28},
pages={856-941}
}
• M. Shulman
• Published 2018
• Computer Science, Mathematics
• Math. Struct. Comput. Sci.
• We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp variables". This yields type theories that we call "spatial" and "cohesive", in which the types can be viewed as having independent topological and homotopical structure. These type theories can then be used to study formally the process by which topology… CONTINUE READING

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