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Some observations on cubical sets

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Cubical sets are similar to simplicial sets, but have squares and cubes in place of triangles and simplices. Recently, they have become a popular topic in homotopy type theory. See for example “A cubical set model of type theory” by Bezem, Coquand and Huber (http://www.cse.chalmers.se/~coquand/mod1.pdf).

In this talk I will show some observations on cubical sets. Firstly, I will briefly introduce (one of the many presentation of) cubical sets. Then I will show a construction producing categories out of cubical sets. By iterating the construction, a (possibly new) structure arises naturally. Finally, the category formed by these new objects is shown to be monadic over cubical sets.

This talk is part of the Junior Category Theory Seminar series.

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