Name for a concept?

Is there an existing name in the literature for a category in which every cospan admits a completion to a commutative square? (Just that, no uniqueness, no universal properties required, just every cospan sits inside at least one commutative square). If so, what have such things been called? If not, does anyone have a poetic idea for a good name for such categories? Best Thoughts, David Yetter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]