Categorical view of the Partite Lemma in structural Ramsey Theory

Sebastian Junge

Published 2022-01-16, updated 2023-01-21Version 2

We construct of the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point of view allows us to unify the direct Partite Lemma in the Ne\v{s}et\v{r}il--R\"odl Theorem with the dual Paritite Lemma by Solecki.