Can anyone help me with the following final coalgebra questions 1. Let X be a fixed Set. What is the final coalgebra of the functor [X,_]:Set -> Set. If you wish to make X finite then that's fine by me. 2. Consider the functor [[_,2],2]:Set -> Set. This functor doesnt have a final coalgebra for cardinality reasons. However one may define a finitary variant of this functor as follows: First let TX = [[X,2],2] if X is finitely presentable. Thus T:Set_fp -> Set is a functor from the full subcategory of fintely presentable objects of Set into Set. Next define T' to be the left Kan extension of T along the inclusion Set_fp -> Set. In other words T'X is the filtered colimit of all the TX_0 where X_0 is a finitely presentable subobject of X Now, T' is clearly finitary and from general nonsense we know that it has a final coalgebra. But what is it concretely? Thanks for any help you can offer Neil 17-Jan-2002 09:04:05 -0400,2670;000000000001-00000000