In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category. Outline of the paper. We present logic (to be more precise: a consequence relation) on an abstract set rather then a set of formulae. We exhibit various ways to encode this structure which have roots in different fields of mathematics,

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... namely topology and (co)algebra. We start by taking a relational approach to the consequence relation; we define appropriated identity and composition to form a monoid that represents the abstract