By Bodo Pareigis

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**Example text**

Proof. 14. T h e functor i n Corollary 1 denoted by 0 will be called the evaluation functor. N o w we want to apply the new results for representable functors. S 44 1. COROLLARY 2. (a) (b) PRELIMINARY NOTIONS Let A,Be

I n ? the distinguished points of Mor^(^4, B) are uniquely determined by the condition that M o r ^ ( / , —) and Mor^(-yg) are pointed set maps. I n the category S an initial object is 0 and a final object is {0}. Zero objects do not exist. T h e only zero morphisms have the form 0 —> A. I n the category S* each set with one point is a zero object. T h u s there are zero morphisms between all objects. Similarly, the set with one point y c 24 1. PRELIMINARY NOTIONS with the corresponding structure is a zero object i n the categories A b , and Top*.

D) | jMor(