An institution isomorphism for planar graph colouring

Maximal planar graphs with vertex resp. edge colouring axe naturally cast as (deceptively similar) institutions. One then tries to embody Tait's equivalence algorithms into morphisms between them, and is lead to a partial redesign of those institutions. This paper aims at introducing a few pragmatic questions which arise in this case study, which also showcases the use of relational concepts and notations in the design of the subject institutions, and gives an outline of a solution to the problem of designing an isomorphism between them.