A small final coalgebra theorem

On universal categories of coalgebras

“…Accessible functors are called small in [28,29,4]. In [1], Adámek and Porst proved that for set functors this notion coincides with what is called a bounded functor in [16,23]. An equivalent formulation best suited for our purposes is that…”

“…In a prevailing trend, notions of universal algebra are dualized to notions of coalgebra theory. In the process, certain similarities but also significant differences are being discovered and widely discussed; see [1,2,11,12,13,16,21,23,26].…”

On the final sequence of a finitary set functor

“…For set functors, accessibility seems to be a common denominator amongst some of the hypotheses involved in the various final coalgebra theorems in the literature, e.g., being bounded in [12] and set-based in [2]. Adámek and Porst [6] have shown that the assumption of boundedness of a set functor is equivalent to accessibility.…”

Universality of Categories of Coalgebras

“…Theory of coalgebras attracted the attention of theoretical computer scientists because of its suitability to capture certain notions and processes, see [9,12,18] for instance. In addition, categorical properties of Coalg F depend on the intrinsic properties of F, and this presents a rich and interesting field of problems.…”