2025/08/15 by Hadek, Maximilian
#05D10 #18A30 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.11465
We prove a new characterization of the Ramsey property of categories in terms of a generalized form of Kőnig's tree lemma. Afterwards, we discuss its applications to structural Ramsey theory. In particular, we provide a new proof of the existence and uniqueness of minimal Ramsey expansions and a new transfer theorem which uses Grothendieck opfibrations and unifies several known Ramsey transfers.