If $A_i, B_i, C_i$ , for $i=1,2,3$ are objects of an abelian category such that there is a commutative diagram
![$\displaystyle \xymatrix{ & 0\ar[d]&0\ar[d]&0\ar[d]&\ 0\ar[r] & A_1\ar[r]\ar[d... ... 0\ar[r] & A_3\ar[r]\ar[d]&B_3\ar[r]\ar[d]&C_3\ar[r]\ar[d]&0\ & 0 & 0 & 0 &}$](http://images.planetmath.org:8080/cache/objects/4597/js/img1.png "$\displaystyle \xymatrix{ & 0\ar[d]&0\ar[d]&0\ar[d]&\ 0\ar[r] & A_1\ar[r]\ar[d... ... 0\ar[r] & A_3\ar[r]\ar[d]&B_3\ar[r]\ar[d]&C_3\ar[r]\ar[d]&0\ & 0 & 0 & 0 &}$")