21 March 2018, Algebra|Coalgebra Seminar, Frederik M. Lauridsen

In 1966 Grätzer introduced the notion of transferability for finite lattices. A finite lattice L is transferable if whenever L has an embedding into the ideal completion of a lattice K, then L already has an embedding into K. In this talk we will introduce the analogous notion of MacNeille transferability, replacing the ideal completion with the MacNeille completion. We will pay particular attention to MacNeille transferability of finite distributive lattices with respect to the class of Heyting algebras. This will also allow us to find universal classes of Heyting algebras closed under MacNeille completions.

This is joint work with G. Bezhanishvili, J. Harding, and J. Ilin.