for C1, C2 being semi-functional para-functional category st the carrier of C1 = F₁() & ( for a, b being Object of C1 holds <^a,b^> = F₂(a,b) ) & the carrier of C2 = F₁() & ( for a, b being Object of C2 holds <^a,b^> = F₂(a,b) ) 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 #)