Finite retracts of Priestley spaces and sectional coproductivity

Abstract

$P$ is sectionally coproductive if the Priestley surjection $\coprod X_i\to P$ induced by Priestley surjections $X_i\to P$ is a retraction only when some of the $f_i$ is a retraction. $P$ is sectionally coproductive iff it is acyclic.

Keywords

• distributive 01-lattice
• Priestley duality
• ultraproduct