Pullbacks of a family of arrows

What is the standard name for the limit of the diagram consisting of a morphism f : A --> C and an I-indexed family of morphisms g_i : B_i --> C where I is a set? This is a slight generalisation of pullbacks. I am really interested in the terminology for the following notion: A class of morphisms M is stable under such generalised pullbacks if, for all such limiting cones a : P --> A b_i : P --> B_i if g_i are all in M, then so is the morphism a : P --> A (This is a slight generalisation of stability of M under pullbacks.) Thanks, Ohad. -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]