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Tagged with nonabelian-cohomology homotopy-theory
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How can one concretely approximate a homotopy type by a scheme or (higher/derived) stack?
What methods are there to approximate an arbitrary homotopy type by an algebraic-geometric object in a concrete (read: computable) way?
I know this is an ambitious question, so maybe I should ...
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Is there a homology theory that gives a *necessary and sufficient* condition for homotopy equivalence?
Is there a (non-Abelian) homology theory that realizes the following:
Let $X,Y$ be manifolds with complexes $C(X),C(Y)$.
Then $X$ and $Y$ are homotopy-equivalent if and only if $C(X)$ and $C(Y)$ ...
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