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2012 Normal and conormal maps in homotopy theory
Emmanuel D. Farjoun, Kathryn Hess
Homology Homotopy Appl. 14(1): 79-112 (2012).


Let $M$ be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of monoids and of conormality for maps of comonoids in $M$. These notions generalize both principal bundles and crossed modules and are preserved by nice enough monoidal functors, such as the normalized chain complex functor.

We provide several explicit classes of examples of homotopynormal and of homotopy-conormal maps, when $M$ is the category of simplicial sets or the category of chain complexes over a commutative ring.


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Emmanuel D. Farjoun. Kathryn Hess. "Normal and conormal maps in homotopy theory." Homology Homotopy Appl. 14 (1) 79 - 112, 2012.


Published: 2012
First available in Project Euclid: 12 December 2012

zbMATH: 1244.55017
MathSciNet: MR2954668

Primary: 18D10 , 18G55 , 55P35 , 55U10 , 55U15 , 55U30 , 55U35

Keywords: homotopical category , monoidal category , normal map , twisting structure

Rights: Copyright © 2012 International Press of Boston


Vol.14 • No. 1 • 2012
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