8.3 of an n-connected space and
Let be a pointed type and . Recall from \autorefthm:homotopy-groups that if the set has a group structure, and if the group is abelian.
If is -truncated and , then for all .
If is -connected and , then for all .
We have the following sequence of equalities:
The third equality uses the fact that in order to use that and the fourth equality uses the fact that is -connected. ∎
The sphere is -connected by \autorefcor:sn-connected, so we can apply \autoreflem:pik-nconnected. ∎
|Title||8.3 of an n-connected space and|