Jason (jcreed) wrote,

Continuing to flail about in HoTT-world. Tried to prove that reduced suspension Σ is right adjoint to the loop-space functor Ω. I thought I was clever by defining the reduced suspension by taking a pointed space, forgetting its point, taking its unreduced suspension, and then saying its basepoint was the north pole of the resulting suspension, thinking this would save me from reasoning about 2-cells. But alas, no, after deciding how to map ΣP → Q to P → ΩQ and back, and proving that their underlying (unpointed) maps compose to the identity, I have an enormous, tangled proof obligation to see that basepoints are mapped homotopically close-enough to basepoints. Not sure how to get around (or even mitigate) this.
Tags: hott, math

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