scheme :: YELLOW21:sch 5
CLCatUniq2{ F₁() -> non empty set , P₁[ object ], P₂[ set , set , set ] } :

for C1, C2 being lattice-wise category st ( for x being LATTICE holds
( x is Object of C1 iff ( x is strict & P₁[x] & the carrier of x in F₁() ) ) ) & ( for a, b being Object of C1
for f being monotone Function of (latt a),(latt b) holds
( f in <^a,b^> iff P₂[a,b,f] ) ) & ( for x being LATTICE holds
( x is Object of C2 iff ( x is strict & P₁[x] & the carrier of x in F₁() ) ) ) & ( for a, b being Object of C2
for f being monotone Function of (latt a),(latt b) holds
( f in <^a,b^> iff P₂[a,b,f] ) ) holds
AltCatStr(# the carrier of C1, the Arrows of C1, the Comp of C1 #) = AltCatStr(# the carrier of C2, the Arrows of C2, the Comp of C2 #)