Peter Easthope points out that in Lawvere & Schanuel there is no mention of Arend Heyting. That is unfortunate, especially since pp 348-352 are devoted to introducing Heyting's Algebras and one of their possible objective origins. The 2nd edition should correct this omission. Summarizing the 16 responses, a common thought of many must have been "If small implies finite then any example must be a poset (category in which any two parallel maps are equal) because of Freyd's theorem. A CC poset is almost by definition a Heying Algebra. There are linearly ordered ones of any size, but if the size is four or more, there are also examples that are not linearly ordered.... On the other hand if infinite examples are allowed, and posetal ones are not, it is hard to think of a CCC smaller than a skeletal category of all finite sets." Bill