# Categorical Approach to Swarm Computations

### Jerzy KrÃ³l, Andrew Schumann, Krzysztof Bielas

#### Abstract

We propose the model approaching the problems of organisation, computing and emergent behavior of certain swarms from category theory point of view. In this model the Yoneda embedding to the category of presheaves spanned over the basic category of partial recursive functions, is activated by external stimuli and the resulting excited domains carry collective self-organising processes. We find that the intuitionistic logic of the presheaf topos becomes a primary logic for a way how swarms act and how they should be described algorithmically.

Download#### Paper Citation

#### in Harvard Style

KrÃ³l J., Schumann A. and Bielas K. (2021). **Categorical Approach to Swarm Computations**.In *Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: Paradigms-Methods-Approaches,* ISBN 978-989-758-490-9, pages 218-224. DOI: 10.5220/0010389502180224

#### in Bibtex Style

@conference{paradigms-methods-approaches21,

author={Jerzy KrÃ³l and Andrew Schumann and Krzysztof Bielas},

title={Categorical Approach to Swarm Computations},

booktitle={Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: Paradigms-Methods-Approaches,},

year={2021},

pages={218-224},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010389502180224},

isbn={978-989-758-490-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: Paradigms-Methods-Approaches,

TI - Categorical Approach to Swarm Computations

SN - 978-989-758-490-9

AU - KrÃ³l J.

AU - Schumann A.

AU - Bielas K.

PY - 2021

SP - 218

EP - 224

DO - 10.5220/0010389502180224