I have a short question concerning terminology related to extensive categories. In the latter, coproducts enjoy the following property. U ----> Z <---- V | | | | | | v v v A ---> A+B <--- B /--------------------------------------------\ | In a double square diagram as illustrated, | | the top row is a coproduct diagram | | if and only if both squares are pullbacks. | \--------------------------------------------/ The "if"-part of this condition is known as universality or pullback-stability of co-products; it also can be formulated for arbitrary colimits. What about the "only if" direction? Is there a name for it in the case of arbitrary colimits? Tobias Heindel [For admin and other information see: http://www.mta.ca/~cat-dist/ ]