Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in the specification language CASL), and (2) of combinations of networks of specifications (in the OMG standardised language DOL). The problem of using colimits ...

ELEMENTARY CLASSES AND ACCESSIBLE CATEGORIES T. BEKE∗ AND J. ROSICKÝ∗∗ Abstract. We investigate properties of accessible categories with directed colimits and their relationship with categories arising from Shelah’s Abstract Elementary Classes. We also investigate ranks of objects in accessible categories, and the effect of accessible functors on ranks. We investigate properties of accessible c...

The notion of an endofunctor having “greatest subcoalgebras” is introduced as a form of comprehension. This notion is shown to be instrumental in giving a systematic and abstract proof of the existence of limits for coalgebras—proved earlier by Worrell and by Gumm & Schröder. These insights, in dual form, are used to reinvestigate colimits for algebras in terms of “least quotient algebras”—lead...

A category of one-step semantics is introduced to unify different approaches to coalgebraic logic parametric in a contravariant functor that assigns to the state space its collection of predicates with propositional connectives. Modular constructions of coalgebraic logic are identified as colimits, limits, and tensor products, extending known results for predicate liftings. Generalised predicat...

The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single universal property in the associated bicategory of spans. To this end, we first provide a general noti...

Injectivity with respect to morphisms having λ-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, λ-directed colimits, and λ-pure subobjects. This sharpens the result of the first two authors (Trans. Amer. Math. Soc. 336 (1993), 785-804). In contrast, for geometric logic an example is found of a class closed under directed col...