let C be category; :: thesis: for o1, o2 being Object of C
for A being Morphism of o1,o2 st A is iso holds
( A is retraction & A is coretraction )
let o1, o2 be Object of C; :: thesis: for A being Morphism of o1,o2 st A is iso holds
( A is retraction & A is coretraction )
let A be Morphism of o1,o2; :: thesis: ( A is iso implies ( A is retraction & A is coretraction ) )
assume A1: A is iso ; :: thesis: ( A is retraction & A is coretraction )
then A * (A ") = idm o2 ;
then A " is_right_inverse_of A ;
hence A is retraction ; :: thesis: A is coretraction
(A ") * A = idm o1 by A1;
then A " is_left_inverse_of A ;
hence A is coretraction ; :: thesis: verum