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- W2022969606 abstract "Any pointed CW-complex X has associated a categorical crossed module WX whose homotopy groups coincide with those of the space up to dimension 3. Here we associate WX more closely with the homotopy 3-type of X. We introduce the nerve of a categorical crossed module L and define its classifying space BL as the geometrical realization of the nerve. Then we prove that there is a map X → BWX inducing isomorphism of the homotopy groups πi for i ≤ 3. Finally, comparison with other algebraic models of 3-types is achieved (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)" @default.
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- W2022969606 date "2010-03-18" @default.
- W2022969606 modified "2023-09-26" @default.
- W2022969606 title "The classifying space of a categorical crossed module" @default.
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- W2022969606 doi "https://doi.org/10.1002/mana.200610827" @default.
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