On descent for coalgebras and type transformations

M Kianpi
2016 unpublished
We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent mor-phisms for coalgebras over toposes in some cases. Also, we study some ex-actness 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
more » ... s 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.