A Single Perspective on Arrows between Institutions

The purpose of this paper is to bring the most important and influential concepts of arrows between institutions, i.e., institution morphisms, plain maps of institutions, simulations, and (simple) maps of institutions into a common perspective. Based on three simple constructions for institutions--reindexing, change of syntax, change of semantics -- we show, firstly, that each of these arrows can be equivalently characterized by the existence of a correspond intermediate institution that is related to both involved institutions syntactically or semantically, respectively. Secondly, we show that taking into account reindexing and restriction of semantics, we can describe any of these arrows as an institution morphism (or dually as a plain map) between institutions of the same scheme. We also discuss the possible role of the intermediate institutions in applications.