Normal and conormal maps in homotopy theory

• Published in: Homology, Homotopy and Applications (ISSN: 1512-0139), vol. 14, num. 1, p. 79-112
• Somerville: Int Press Boston, Inc, 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.

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

Reference

• EPFL-ARTICLE-181974
• doi:10.4310/HHA.2012.v14.n1.a5
• View record in Web of Science

Record created on 2012-10-30, modified on 2017-05-12