Farjoun, Emmanuel D.
Hess, Kathryn
Normal and conormal maps in homotopy theory
Homology, Homotopy and Applications
Homology, Homotopy and Applications
Homology, Homotopy and Applications
Homology, Homotopy and Applications
34
14
1
Normal map, monoidal category, homotopical category, twisting structure
2012
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 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.
Int Press Boston, Inc
1512-0139
Homology, Homotopy and Applications
Journal Articles
10.4310/HHA.2012.v14.n1.a5