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It seems modal logic is in fact a sheaf/presheaf and WTF: https://arxiv.org/pdf/1403.0020.pdf
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I realized that there is also "Categories for the Working Philosopher" and the book was very interesting. It was definitely for mathematicians who do / are interested in mathematical philosophy and not for general public (such as continental philosophers lol) though.
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refind self looks very interesting. thanks for sharing