Corollary 5.97.
We have
\[(P_n\textup{-equiv})(P_m\textup{-equiv})
=
(P_{n+m+1}\textup{-equiv}).\]
Proof
Under the identification above, this is the equality
\[K^{n+1}K^{m+1}=K^{n+m+2}.\]
See also [Anel et al. 2018, Theorem 3.3.4(4)].References
- Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal. Goodwillie's calculus of functors and higher topos theory. J. Topol., 11 (4), 1100–1132. 2018.