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Henry Story (Dec 29 2020 at 22:09):While reading about higher dimensional networks I came to read up more about simplicial sets. Finding them to be used in interesting ways in epistemic modal logic sparked my interest enough to read enough about them to get a reasonable intuition. Then I realized they had been used by David Spivak in his work on Simplicial Databases, and discovered that that was the first thing discussed in Emilie Riehl's book on Elements of ∞-Category Theory.
That is when I remembered that I had come across them reading HoTT, and that Cubical Sets were playing the same role in Cubical HoTT.
Is there an introduction to cubical sets that is as approachable as the paper An elementary illustrated introduction to simplicial sets by Greg Friedman?
Amar Hadzihasanovic (Dec 30 2020 at 07:39):"Cubical sets and their site" by Grandis and Mauri is a very good introduction in my opinion. It gives many different, useful viewpoints on the categories of cubes.
Amar Hadzihasanovic (Dec 30 2020 at 07:40):Not sure how it compares to Friedman as I haven't read it.