Address. Department of Mathematics, University of Bremen, 28359 Bremen, Germany
Abstract. It is shown that the categories of $R$-coalgebras for a commutative unital ring $R$ and the category of $A$-corings for some $R$-algebra $A$ as well as their respective categories of comodules are locally presentable.
AMSclassification. Primary 16W30, Secondary 18C35.
Keywords. Coalgebras, comodules, locally presentable categories.