  We propose the notion of association schemoids generalizing that of
association schemes from small categorical points of view. In particular, a
generalization of the Bose-Mesner algebra of an association scheme appears as a
subalgebra in the category algebra of the underlying category of a schemoid. In
this paper, the equivalence between the categories of grouopids and that of
thin association schemoids is established. Moreover linear extensions of
schemoids are considered. A general theory of the Baues-Wirsching cohomology
deduces a classification theorem for such extensions of a schemoid. We also
introduce two relevant categories of schemoids into which the categories of
schemes due to Hanaki and due to French are embedded, respectively.
