The homomorphism S which, according to the snake lemma, permits construction of an exact sequence Ker(α)⟶Ker(β)⟶Ker(γ)⟶^S coker(α)⟶coker(β)⟶coker(γ) from the above commutative diagram with exact rows. The homomorphism S is defined by S(c) = a' + Im(α) for all c element Ker(γ), Im denotes the image, and a' is obtained through the following construction, based on diagram chasing. 1. Exploit the surjectivity of g to find b element B such that c = g(b).

cokernel | commutative diagram | diagram chasing | exact sequence | group kernel | snake lemma