42 citations
- Evan Patterson2 profiles10 · h 12
- David I. Spivak2 profiles6 · h 27
- James P. Fairbanks5 · h 10
- Sophie Libkind2 profiles4 · h 6
- Andre Baas3 · h 5
- Owen Lynch2 profiles3 · h 3
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- J. Baez2 · h 57
- Michael Lambert2 · h 1
- Timothy Hosgood2 profiles2 · h 1
- T. S. C. Smithe2 · h 6
- T. St. Clere Smithe2 · h 0
- ToposUS24 papers
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- Georgia Tech Research Institute3 papers
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- University of California, RiversideUS2 papers
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- Utrecht UniversityNL2 papers
- Centre for Quantum TechnologiesSG1 paper
- Cornell UniversityUS1 paper
- Eindhoven University of TechnologyNL1 paper
- Freie Universität BerlinDE1 paper
4 papers · 2 filters
Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing
Toby St. Clere Smithe
We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebrai…
Dialectica Principles via Gödel Doctrines
Davide Trotta, Matteo Spadetto, Valeria de Paiva
Gödel's Dialectica interpretation was conceived as a tool to obtain the consistency of Peano arithmetic via a proof of consistency of Heyting arithmetic in the 40s. In recent years…
Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets
Brandon T. Shapiro, David I. Spivak
Natural organized systems adapt to internal and external pressures and this happens at all levels of the abstraction hierarchy. Wanting to think clearly about this idea motivates o…
Polynomial Functors and Shannon Entropy
David I. Spivak
Past work shows that one can associate a notion of Shannon entropy to a Dirichlet polynomial, regarded as an empirical distribution. Indeed, entropy can be extracted from any d:Dir…