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Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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Reference for choosing a path lifting function?
I recall having seen discussion of a Hurewicz or Serre fibration
equipped with a chosen path lifting function. Citation??
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Universal bundles for monoids versus groups
Dold and Lashof compare their construction for a monoid M to Milnor's
when M is a group G. They give an explicit comparison for the first stage of the constructions. Somewhere I've seen the general n- …