Behavioural Satisfaction and Equivalence in Concrete Model Categories

We use the well-known framework of concrete categories to show how much of standard universal algebra may be done in an abstract and still rather intuitive way. This is used to recast the unifying view of behavioural semantics of speciications based on behavioural satisfaction and, respectively, on behavioural equivalence of models abstracting away from many particular features of standard algebras. We also give an explicit representation of behavioural equivalence between models in terms of behavioural correspondences.