Abstract

We give an axiomatic account of what structure on a category C and an endofunctor H on C yield similar structure on the category H0Coalg of H-coalgebras. We give conditions under which completeness, cocompleteness, symmetric monoidal closed structure, local presentability, and subobject classifiers lift. Our proof of the latter uses a general result about the existence of a subobject classifier in a category containing a small dense subcategory. Our leading example has C = Set with H the endofunctor for which a coalgebra is a finitely branching (labelled) transition system. We explain that example in detail. 1 Introduction Given an endofunctor H on the category Set, an H-coalgebra is a set X together with a function x : X 0! HX. A leading example of such an H is given by the functor P ! that takes a set X to the set of finite subsets of X , with the behaviour of H on maps given by direct image. An H-coalgebra is then a finitely branching transition system. A variant, is given by sta...

Citations