Justin Pearson asks:
Some books ... say that a CCC has a finite limits plus ... exponentials. ... other books seem to define it as finite products plus exponentials. ... can you get finite limits from finite products ... ?
Just as Eilenberg's "co-six" category (all sets / or all finite sets / of cardinality other than 6 ) provides an example of a closed category that's not (but is almost) cartesian closed, so what one might call "co-five" (all sets / or all finite sets / of cardinality other than 5 ) provides an example of a cartesian closed category (in the second sense) not having all equalizers (so not finitely complete). For some purposes one cares not a fig about the presence/absence of finite limits (other than products, of course) -- for other purposes one cares a lot. [Of course almost any prime could have been used in place of the prime 5 .] Fred E.J. Linton Wesleyan U. Math. Dept. 649 Sci. Tower Middletown, CT 06459 E-mail: <FLINTON@eagle.Wesleyan.EDU> ( or <fejlinton@{att|mci}mail.com> ) Tel.: + 1 203 776 2210 (home) or + 1 203 347 9411 x2249 (work)