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Category Theory

ACT2Infer 2024

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Programming Languages

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Jupyter Notebook Exhibit⁠

with thanks to Ryan Buchanan (KU)

From “Shared Protention” — 3 things.

States, Actions, Reflections.

Lots of work on Polynomial Functors:

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https://toposinstitute.github.io/poly/poly-book.pdf⁠

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https://github.com/ToposInstitute/poly⁠

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https://ncatlab.org/nlab/show/polynomial+functor⁠

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https://topos.site/blog/2022-08-04-poly-pale-reflection-proly/⁠

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https://www.youtube.com/watch?v=tKVTmBdXSdk⁠

Polynomial functors: Lecture 2/9

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Using Poly in experiments with

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https://github.com/biaslab/LAIF⁠

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Realising Synthetic Active Inference Agents (LAIF)⁠

in RxInfer.jl in Julia

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Corolla Forrest & Trees

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https://arxiv.org/abs/1801.04337⁠

Forest Categories

Eugenio Moggi: "Categories of Classes for Collection Monads"

https://www.youtube.com/watch?v=Jl7FTOaFZgA⁠

at the Topos Institute. This discusses “Categories that are suitable for databases”. Very interesting & may relate to databases for e.g. for well-typed ActInf things/ecosystems, cognitive models/frameworks/tools/methods, etc....

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http://logica.dipmat.unisa.it/incontro-aila2014/uploads/1/8/0/6/18064313/paper_5.pdf⁠

Categories for Collection Types Eugenio Moggi

Could this “Collections” approach be related to the work of Ryan on the Museum?

There seem like many interesting pieces which could be connected more rigorously as well as translated into tangible/extant realizations.

E.g. Collection Monads

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More on Monads:

https://www.cs.cornell.edu/courses/cs6110/2011sp/lectures/lecture37.pdf⁠

as collections/categories.

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https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/abs/implementing-collection-classes-with-monads/4944443869B1C6A4F8A802B82C3ABFB0⁠

“Heuristically, the axioms defining a collection monad state that each collection has a finite set of members of X, that pure 1-element collections exist and that a collection of collections flattens to a single collection whose members are the union of the members of the constituent collections. The relationship between monads and universal algebra leads to a formal definition of collection implementation in terms of tree-processing. ”

Notions of computation and monads, Eugenio Moggi — early and well-cited 1991 paper.

Curation & datasets. And — Why is a dataset considered real? What about them is real?

How can we have high integrity information supply chain?

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Qubit Onion⁠

and adjunctions.

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