for C being Category
for O being non empty Subset of the carrier of C
for M being non empty set
for d, c being Function of M,O
for p being PartFunc of [:M,M:],M
for i being Function of O,M st M = union { (Hom (a,b)) where a, b is Object of C : ( a in O & b in O ) } & d = the Source of C | M & c = the Target of C | M & p = the Comp of C || M holds
CatStr(# O,M,d,c,p #) is full Subcategory of C