Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 5 1 2016 07 01 On descent for coalgebras and type transformations 103 130 13904 EN Maurice Kianpi Laboratory of Algebra, Geometry and Applications, Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812, Yaounde, Republic of Cameroon. Journal Article 2016 03 17 We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between corresponding categories of coalgebras.  As a result, we find conditions under which the induced functors preserve natural number objects as well as a criterion for them to be exact. Also this enable us to give a criterion for split epis in a category of coalgebras to be effective descent. https://cgasa.sbu.ac.ir/article_13904_256ff9427762d0a23812c1c6b36d9b48.pdf