for C1, C2 being semi-functional para-functional category st the carrier of C1 = F₁() & ( for a, b being Element of F₁()
for f being Function holds
( f in the Arrows of C1 . (a,b) iff ( f in Funcs (F₂(a),F₂(b)) & P₁[a,b,f] ) ) ) & the carrier of C2 = F₁() & ( for a, b being Element of F₁()
for f being Function holds
( f in the Arrows of C2 . (a,b) iff ( f in Funcs (F₂(a),F₂(b)) & 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 #)