Synthetic homotopy theory (Rev #3)

See open problems

- Homotopy pushout $Y \sqcup^X Z$
- Join? $X * Y$
- Suspension $\Sigma X$
- Homotopy fiber?
- Smash product $X \wedge Y$

- Eilenberg Maclane spaces? $K(G,n)$
- James construction $J(X) \simeq \Omega \Sigma X$
- Hopf construction H-space on $A$ gives fibration $A \to A * A \to \Sigma A$
- Localization
- Whitehead product
- Homology?
- Cohomology $H^n(X;A) \equiv \| X \to K(G,n) \|_0$
- loop space of a wedge of circles

category: homotopy theory