:: deftheorem Def4 defines lattice-wise YELLOW21:def 4 :
for C being category holds
( C is lattice-wise iff ( C is semi-functional & C is set-id-inheriting & ( for a being Object of C holds a is LATTICE ) & ( for a, b being Object of C
for A, B being LATTICE st A = a & B = b holds
<^a,b^> c= MonFuncs (A,B) ) ) );