%0 Journal Article %T Modal representation of coalgebras over local BL-algebras %J Journal of Algebraic Hyperstructures and Logical Algebras %I University of Hatef (Hatef College University) %Z 2676-6000 %A Nganteu, C.T. %A Kianpi, M. %A Amassayoga, O. %D 2021 %\ 11/01/2021 %V 2 %N 4 %P 51-62 %! Modal representation of coalgebras over local BL-algebras %K Kripke frame %K coalgebra %K local BL-algebra %R 10.52547/HATEF.JAHLA.2.4.5 %X We consider the category Coalg(∏) of ∏-coalgebras where ∏ is the endofunctor on the category of local BL-algebras and  L-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(∏). %U https://jahla.hatef.ac.ir/article_141745_545d45b8753d536e59470f810393bb2e.pdf