Natural transformations

Category-theoretic approaches to semantic technologies

Published in James Juniper, The Economic Philosophy of the Internet of Things, 2018

This category-theoretic approach is closely related to the process-oriented research of Kissinger and Uijlen (2017) into the semantics of causal structures, and David Myers’ (2017) on string diagrams for double categories, which he shows to be well-suited to analysis of sets, functions, and relations. Other relevant graph-theoretic research includes Koch et al.’s (2010) work on formalizing opetopes using a combination of nested rings and trees. Significantly, this same formalism was also utilized by the late Robin Milner (2009) in his efforts to integrate the (asynchronous) Pi calculus with Petri nets. The additional structure to account for natural transformations of representative functors is provided by 2-categories.

Constructing condensed memories in functorial time

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Published in Journal of Experimental & Theoretical Artificial Intelligence, 2023

Shanna Dobson, Chris Fields

• Composition of arrows arises, given pro-objects , , and of , by applying the limit functor for diagrams to the natural transformation of functors , given by composition in .

A categorical view of Poincaré maps and suspension flows

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Published in Dynamical Systems, 2022

Tomoharu Suda

A natural transformation η from F to G is denoted by A natural transformation η is a natural isomorphism if is an isomorphism in for each X in

Natural transformations

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Category-theoretic approaches to semantic technologies

Constructing condensed memories in functorial time

A categorical view of Poincaré maps and suspension flows