:: deftheorem Def10 defines -INF(SC)_category WAYBEL34:def 10 :
for W being non empty set
for b₂ being non empty strict subcategory of W -INF_category holds
( b₂ = W -INF(SC)_category iff ( ( for a being Object of (W -INF_category) holds a is Object of b₂ ) & ( for a, b being Object of (W -INF_category)
for a9, b9 being Object of b₂ st a9 = a & b9 = b & <^a,b^> <> {} holds
for f being Morphism of a,b holds
( f in <^a9,b9^> iff @ f is directed-sups-preserving ) ) ) );