# Categorial subsystem independence as morphism co-possibility

## TL;DR

This paper introduces a categorical notion of subsystem independence based on morphism co-possibility, generalizing algebraic quantum field theory concepts to abstract categories and C*-algebras.

## Contribution

It formalizes subobject independence in general categories and applies it to C*-algebras, linking it to relativistic locality in quantum field theory.

## Key findings

- Subobject independence characterized by morphism co-possibility.
- Application to C*-algebras with completely positive maps.
- Proposes a natural subsystem independence axiom for quantum locality.

## Abstract

This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C* algebras with respect to operations (completely positive unit preserving linear maps on C*-algebras) as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory.