Subalgebra Independence
Category Theory
2023-06-21 v1 Mathematical Physics
Logic
math.MP
Abstract
Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when directly applied to classical algebras, subobject independence is not entirely satisfactory. The sole purpose of this note is to introduce the notion of subalgebra independence, which is a slight variation of subobject independence, yet this modification enables us to connect subalgebra independence to more traditional notions of independence. Apart from drawing connections between subalgebra independence and coproducts and congruences, we mainly illustrate the notion by discussing examples.
Cite
@article{arxiv.2306.11659,
title = {Subalgebra Independence},
author = {Zalán Gyenis and Alexa Gopaulsingh and Övge Öztürk},
journal= {arXiv preprint arXiv:2306.11659},
year = {2023}
}