Information entropy re-defined in a category theory context using preradicals

Sebastian Pardo G.; Gabriel A. Silva

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arXiv · 2112.06034

Information entropy re-defined in a category theory context using preradicals

Sebastian Pardo G.·Gabriel A. Silva

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Abstract

Algebraically, entropy can be defined for abelian groups and their endomorphisms, and was latter extended to consider objects in a Flow category derived from abelian categories, such as $R\textit{-}Mod$ with $R$ a ring. Preradicals are endofunctors which can be realized as compatible choice assignments in the category where they are defined. Here we present a formal definition of entropy for preradicals on $R$-Mod and show that the concept of entropy for preradicals respects their order as a big lattice. Also, due to the connection between modules and complete bounded modular lattices, we provide a definition of entropy for lattice preradicals, and show that this notion is equivalent, from a functorial perspective, to the one defined for module preradicals.

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BibTeX RIS

Sebastian Pardo G., Gabriel A. Silva. 2021-12-11. Information entropy re-defined in a category theory context using preradicals. https://arxiv.org/abs/2112.06034

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