Category Theory for Genetics

TL;DR

This paper develops a categorical framework to model various genetic concepts such as DNA sequencing, CRISPR, and haplotypes, enabling a unified mathematical language for genetics.

Contribution

It introduces a new categorical language based on limit-sketches to model genetic phenomena, connecting biological concepts through universal properties.

Findings

Models in sets represent genetic material.

Models in modules represent haplotypes.

A universal property relates the two classes of models.

Abstract

We introduce a categorical language in which it is possible to talk about DNA sequencing, alignment methods, CRISPR, homologous recombination, haplotypes, and genetic linkage. This language takes the form of a class of limit-sketches whose categories of models can model different concepts of Biology depending on what their categories of values are. We discuss examples of models in the category of sets and in the category of modules over the Boolean semi-ring $\{0,1\}$. We identify a subclass of models in sets that models the genetic material of living beings and another subclass of models in modules that models haplotypes. We show how the two classes are related via a universal property.