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**Example text**

4. 53 - Other examples. In this section we consider a few other examples tional algebras although the preceding. The simplest = (I,l,1). x~x functions. relation, It is perhaps that the algebras, ~, gory of preordered + denotes category called a preordered to note as before, sets. (T,~,~) The category subcate- A relational xIX and xI1. where TX = X+l, of algebras algebra Now X+l is a coproduct law requires and so x is deter- The first restriction (as soon as xlX is a preorder) that X ° be a ray.

In abelian categories, (La Jolla 1965), AdJunctlon Closed categories, Proc. Conf. on 1966), 95 - 120. for enriched categories, Reports of the Midwest Category Seminar III (Lecture Notes in Mathematics, Volume 106, 1969), 166 - 177. , On monads in symmetric monoldal closed categories, Aarhus Universitet~ Preprint Series 1967/68, No. ). , Closed categories Aarhus Unlversitet~ generated by commutative monads, Preprint Series 1968/69, No. 13 (to appear in J. Austr. Math. ). , Category Theory, 1 (Lecture Notes in Volume 86, 1969), 76 - 122.

Transitive, in no case are the results of rela- Thus the algebras set and X ° is a ray. the order as well. apply to the category of relational of the triple where TX is the set of ultrafilters on X+l. o $4 o The algebras are pairs (X,Xo) where X is a topological space and XoC X is a closed subspace. Mappings are continuous maps of pairs No other interesting examples are known to us. It seems fairly clear that Cat, for example, is a full subcategory of the relational models of the theory of monoids (however the nullary operation 1 becomes the set of objects of a categoryl) but just being a full subcategory is not very informative.