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Published online by Cambridge University Press: 21 April 2021
We show that the concept of entropy is inescapable even in “pure” branches of mathematics such as algebra, topology and category theory. Specifically, we describe an entirely general categorical construction which, when given the real line and the standard simplices as inputs, produces Shannon entropy as the output. The construction involves operads and their algebras. We then show how this categorical line of thinking leads naturally to the entirely concrete and explicit characterization of information loss in Chapter 10.
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