1. basics of ω-teisi, don't have precise definition. In particular, dimension raising of composition. 2. Delooping: define k-monoidal ω-tas as ω-tas with one (k-1)-arrow, and k-monoidal nD tas as (n+k)D tas with one (k-1)-arrow. View as nD tas with extra structure. Inclusion is \Sigma^k. 3. Looping: from pointed ω-tas C, make C(id^k-1_c, id^k-1_c), which is k-monoidal, call this ω^k. \Sigma^k -| ω^k. 4. Suspension: underlying functor forgetting k-monoidal structure. Left adjoint to this, giving free k-monoidal structure, is suspension. 5. Baez-Dolan's stabilization hypothesis (rephrased for teisi): S: (k+2)-monoidal kD teisi → (k+3)-monoidal kD teisi is iso. proof: follows immediately by checking the dimension raising of (k+3)-monoidal structure. So stabilization *theorem* is easy consequence of basics of ω-teisi. 6. This will be sections 2.6.1 - 2.6.3 of the forthcoming 80+ page paper “Central observations on ω-teisi”.