Abstract
Quillen’s famous Theorem B describes the homotopy fiber ofBF :B C/arB, wheref :C is a functor andB the classifying space functor. This is here generalized to a description of the homotopy fiber ofB(F,α,β) :B(Y C,X)/ar(Y/t' C/t',X/t') where (F,α,β) : (Y C,X)/ar(Y/t' C/t',X/t') is a mapping of 2-sided bar construction data.
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Meyer, JP. Mappings of bar constructions. Israel J. Math. 48, 331–339 (1984). https://doi.org/10.1007/BF02760632
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DOI: https://doi.org/10.1007/BF02760632