Mike complains when he quotes me as saying: ``The relevant property [of Set] is that all non-zero objects be injective.'' His point is that I am using other properties of the category. Of course I was. I thought I was writing in the context of topoi. (Mike does seem to understand that I was writing in the context of locally complete categories, indeed, he wants to use more local completeness than I was willing to use.) He further writes: The problem is that the composite K >--> A x B --> A isn't necessarily monic.. Given the definition of K and the condition on T it is necessarily monic. I should note here that the argument I gave says that the category of countable sets is an algebraically complete category, that is, every endofunctor has an initial algbra. Adamek has already observed that every endofunctor has an invariant object. His other similar examples work as well: for any cardinal the category of all sets of that cardinality or less is algebraically complete; the category of all vector spaces (for a chosen field) of dimension that cardinality or less is algebraically complete (using the axiom of choice in the non-countable cases). ==============================