Information entropy redefined 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:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.06034
 Bibcode:
 2021arXiv211206034P
 Keywords:

 Mathematics  Category Theory;
 Computer Science  Information Theory
 EPrint:
 25 pages