Can anyone supply a reference to the fact that if you add to the hypotheses of a calculus of right fractions the assumption that if {s_i: X_i --> Y_i} is a family of arrows, all in Sigma, then so is \prod s_i: \prod X_i --> \prod Y_i, then you can conclude that if the original category has all limits, so does the fraction category and the canonical functor to the fraction category preserves them.

A relevant reference in the case of finite products is Brian Day, Note on monoidal localisation, Bulletin Australian Math Soc Volume 8 (1973) 1 - 16. Brian called a class S of arrows s in a monoidal category V a monoidal class when s * X and X * s are both in the class when s is. Then the localisation V[S^-1] becomes monoidal with tensor-product preserving projection. The result you state was surely known to Brian and others (such as Harvey Wolff) and may even occur in Brian's work, but I don't have time now to scan his work. I'll ask him when next I talk to him. Regards, Ross +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++