[Freyd-Mitchell][1] and [Gabriel-Popescu][2] theorems, and also the characterization of [co-Grothendieck cats][3]. [1]: http://en.wikipedia.org/wiki/Mitchell_embedding_theorem [2]: http://www.anstuocmath.ro/mathematics/pdf21/17.pdf [3]: http://www.ams.org/bull/1969-75-06/S0002-9904-1969-12431-6/S0002-9904-1969-12431-6.pdf