Modal representation of coalgebras over local BL-algebras

Abstract

We consider the category Coalg( ∏ ) of ∏ -coalgebras where ∏ is the endofunctor on the category of local BL-algebras and BL-morphisms which assigns to each local BL-algebra its quotient by its unique maximal filter and we characterize homomorphisms and subcoalgebras in Coalg( ∏ ) . Moreover, we introduce local BL-frames based on local BL-algebras, and show that the category of local BL-frames is isomorphic to Coalg( ∏ ).