Information entropy re-defined in a category theory context using preradicals
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2021
- DOI:
- 10.48550/arXiv.2112.06034
- arXiv:
- arXiv:2112.06034
- Bibcode:
- 2021arXiv211206034P
- Keywords:
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- Mathematics - Category Theory;
- Computer Science - Information Theory
- E-Print:
- 25 pages