:: deftheorem Def15 defines " CAT_1:def 17 :
for C being Category
for a, b being Object of C
for f being Morphism of a,b st f is invertible holds
for b₅ being Morphism of b,a holds
( b₅ = f " iff ( f * b₅ = id b & b₅ * f = id a ) );