Defines Hausdorff-style and Wasserstein-style metrics on C-sets, proving the latter are convex relaxations of the former and computable as linear programs.
Category theory for scientists (Old version)
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based. For example, monoids are framed in terms of agents acting on objects, sheaves are introduced with primary examples coming from geography, and colored operads are discussed in terms of their ability to model self-similarity. A new version with solutions to exercises will be available through MIT Press.
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The paper uses functors and a pushout in category theory to derive a schema S for John Cage's Silent piece from categories representing specific compositions.
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Hausdorff and Wasserstein metrics on graphs and other structured data
Defines Hausdorff-style and Wasserstein-style metrics on C-sets, proving the latter are convex relaxations of the former and computable as linear programs.
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A category-theoretic approach to modeling John Cage's Silent piece
The paper uses functors and a pushout in category theory to derive a schema S for John Cage's Silent piece from categories representing specific compositions.
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