Projective biframes: a general view

Abstract

We begin with the notion of K-flat projectivity. For each biframe L we then introduce a binary relation ◃L on it. The K-flat projective biframes are exactly such biframes with each element a of the total (first, second) part approximated by the elements x of the total (first, second) part, x◃_L a and the relation ◃_L being stable wrt. the meet operation on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective biframes as those biframes having a coalgebra structure for the K-comonad. The K-coherent biframes and K-flat projective biframes are coreflective in all biframes.

Financial support of the Grant Agency of the Czech Republic under the grant No. 201/06/0664 and of the Ministry of Education of the Czech Republic under the project MSM0021622409 is gratefully acknowledged.