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user 39304
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
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Defining hom spaces in the derived category as limits of hom spaces in the homotopy category
This is actually a standard property of the homotopy category of complexes on which construction of the derived category is based, formulated in unusual way.
For a quasi-isomorphism $s:X'\to X$ and $ …
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