Ara's definition of n-quasi-category uses spines rather than inner horns. It is the best definition for what he does (comparing his model structure to Rezk's one for Θ_n-spaces), but not for combinatorics. The main result of this talk is that for n=2 there is an alternative characterisation using inner horns which is combinatorially more tractable. But I will not really talk about how I proved it, and instead explain how Oury constructed these horns.