Abstract

We present a locally finitely presentable category with a finitely presentable regular generator G and a finitely presentable object A, such that is not a coequalizer of morphisms whose domains and codomains are finite coproducts of objects in G, thereby settling a problem by Gabriel and Ulmer. We also show that in - orthogonality classes in Alg S (category of S-sorted -algebras) for a -ary signature , -presentable objects have a presentation by less than generators and relations and use this to exhibit an example of a reflective subcategory of a locally finitely presentable category which is closed under directed colimits, but not a @ 0 - orthogonality class, disproving a characterization of -orthogonality classes in the book by Ad'amek and Rosick'y.

Citations