Simplicial effects and weakly associative partial groups
Category Theory
2025-02-11 v1 Quantum Physics
Abstract
In this paper, we introduce a new category of simplicial effects that extends the categories of effect algebras and their multi-object counterpart, effect algebroids. Our approach is based on relaxing the associativity condition satisfied by effect algebras and, more generally, partial monoids. Within this framework, simplicial effects and weakly associative partial groups arise as two extreme cases in the category of weak partial monoids. Our motivation is to capture simplicial structures from the theory of simplicial distributions and measurements that behave like effects.
Cite
@article{arxiv.2502.05958,
title = {Simplicial effects and weakly associative partial groups},
author = {Cihan Okay and Victor Castillo and Walker H. Stern},
journal= {arXiv preprint arXiv:2502.05958},
year = {2025}
}
Comments
45 pages, 4 figures