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