The necklace can be obtained from a circle by attaching $n$ 2spheres $S^2$ along arcs, so the necklace $N(n,S^1,a_i)$ is homotopy equivalent to the space obtained by attaching $n$ 2spheres $S^2$ to a circle $S^1$ at points $a_i$ where $i \in [1,n]$. My question is how to construct the necklace $N(n,S^1,a_i)$ in homotopy type theory.
closed as unclear what you're asking by Vladimir Dotsenko, Wolfgang, Marco Golla, JanChristoph SchlagePuchta, Peter Humphries Dec 17 '15 at 23:17
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$\begingroup$ Can you include how you might set up notation for this in homotopy type theory, to set some conventions for answers? $\endgroup$ – j0equ1nn Dec 17 '15 at 7:16
My guess would be
Inductive Necklace (n:nat) :=
 strand : Circle > Necklace
 bead : forall (k:nat), k<n > Sphere2 > Necklace
 attach : forall (k:nat) (p:k<n), strand base = bead k p base2.