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    Christoph Dorn

    Christoph Dorn

    Researcher at Vaticle.

    • United Kingdom
    • Vaticle
    • Oxford Math
    • Oxford CS
    • Cambridge Math
    • ETH Physics
    • GitHub
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    An invitation to geometric higher categories (external link)

    first published 13 Mar 2023

    Fast and mathematically self-contained introduction to basic ideas in geometric higher category theory, written up as an article for the n-Category Café.

    Direct Link

    Tags: very-serious

    Categories: Geometric Higher Categories, Mathematics, Research

    Updated: 13 Mar 2023

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    Pattern matching is an ubiquitous tool in theoretical computer science and type-theoretical mathematics, as well as the formalization of formal languages themselves. We briefly review its role in these subjects, giving examples along the way. We then motivate a deeper connection between pattern matching and higher-dimensional geometry, and suggest how geometric type theory, while not a real type theory yet, tries to provide a general formal framework in which mathematics can be built from higher-dimensional patterns. → read note

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    Comments first published 21 Feb 2023

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    We allow ourselves to speculate a bit about how the 1-dimensional logical constructs that one frequently encounters in practical approaches to mathematical foundations may in fact emerge from a set of “more fundamental” principles of compositionality in higher-dimensional logic. → read note

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