Re: Mac Lane's inclusions

Robert W. McGrail wrote:

Correct me if I am wrong, but it seems to me that every \tau-category is a category with inclusions. Moreover, I recall a result by Freyd that every (sufficiently small? cartesian?) category is equivalent to a \tau-category. The proof does not use choice.

There is certainly a similarity. Tau categories are cartesian categories (categories with all finite limits) which not only have selected monics but also selected jointly-monic n-tuples for all finite n; and all these things compose. Freyd shows every cartesian category is equivalent to a tau category. My construction seems very like Peter's but shortened by working only on monics and not jointly monic lists, and never using limits. best, Colin