“There is a functorwhere
is the homotopy category for unbased spaces , and a natural transformation
that asssigns a
-complex
and a weak equivalence
to an arbitrary space
, such that the following diagram commutes:
and(viz. p. 75 in ref. [1]).is unique up to homotopy equivalence.”
is an isomorphism.
Furthermore, the homotopy groups
of the
-complex
are the colimits of the
homotopy groups of
and
is a group epimorphism.
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