Five-Lemma

Let be an abelian category and

a diagram where both rows are exact and

1. are isomorphisms
   
2. is a monomorphism
   
3. is an epimorphismd
   

Then is also an isomorphism

corollary of:

1. Four-Lemma of epimorphisms
   
2. Four-Lemma of monomorphisms
   
3. abelian category as balanced category
   

• five lemma for groups