Category Theory for Genetics

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.