nLab
rectification

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Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

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see also algebraic topology

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In homotopy theory and in higher category theory by rectification one (usually, often) means the equivalent presentation of a homotopy-coherent structure equivalently by apparently more naive “strict” data.

Many or most rectification statements are examples of the general Rectification theorem for algebras over an operad which states sufficient conditions for the category of algebras over an operad to already be Quillen equivalent to that of the corresponding ∞-algebras over an (∞,1)-operad.

This includes notably Vogt's theorem on the rectification of homotopy coherent diagrams.

Created on September 4, 2013 14:00:49 by Urs Schreiber (212.238.84.235)