On cubical homotopy type theory implemented in the proof assistant Cubical Agda:
Andrea Vezzosi, Anders Mörtberg and Andreas Abel, Cubical Agda: A Dependently Typed Programming Language with Univalence and Higher Inductive Types, 2019 (pdf)
Anders Mörtberg, Cubical methods in HoTT/UF, 2019 (pdf)
Exposition in view of synthetic homotopy theory:
On ordinary cohomology in homotopy type theory:
Guillaume Brunerie, Axel Ljungström, Anders Mörtberg, Synthetic Integral Cohomology in Cubical Agda, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) 216 (2022) doi:10.4230/LIPIcs.CSL.2022.11
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