Normal and conormal maps in homotopy theory

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 inM. 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.


Published in:
Homology, Homotopy and Applications, 14, 1, 79-112
Year:
2012
Publisher:
Somerville, Int Press Boston, Inc
ISSN:
1512-0139
Keywords:
Laboratories:




 Record created 2012-10-30, last modified 2018-03-17

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