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Homotopy theory

{For simple homotopy type, see 57Q10}
55P05 Homotopy extension properties, cofibrations
55P10 Homotopy equivalences
55P15 Classification of homotopy type
55P20 Eilenberg-Mac Lane spaces
55P25 Spanier-Whitehead duality
55P30 Eckmann-Hilton duality
55P35 Loop spaces
55P40 Suspensions
55P42 Stable homotopy theory, spectra
55P43 Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
55P45 ${H}$-spaces and duals
55P47 Infinite loop spaces
55P48 Loop space machines, operads [See also 18D50]
55P55 Shape theory [See also 54C56, 55Q07]
55P57 Proper homotopy theory
55P60 Localization and completion
55P62 Rational homotopy theory
55P65 Homotopy functors
55P91 Equivariant homotopy theory [See also 19L47]
55P92 Relations between equivariant and nonequivariant homotopy theory
55P99 None of the above, but in this section