000181974 001__ 181974
000181974 005__ 20190416055812.0
000181974 022__ $$a1512-0139
000181974 02470 $$2ISI$$a000306939500005
000181974 0247_ $$2doi$$a10.4310/HHA.2012.v14.n1.a5
000181974 037__ $$aARTICLE
000181974 245__ $$aNormal and conormal maps in homotopy theory
000181974 269__ $$a2012
000181974 260__ $$aSomerville$$bInt Press Boston, Inc$$c2012
000181974 300__ $$a34
000181974 336__ $$aJournal Articles
000181974 520__ $$aLet 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.
000181974 6531_ $$aNormal map, monoidal category, homotopical category, twisting structure
000181974 700__ $$aFarjoun, Emmanuel D.
000181974 700__ $$0240499$$aHess, Kathryn$$g105396
000181974 773__ $$j14$$k1$$q79-112$$tHomology, Homotopy and Applications
000181974 8564_ $$s397450$$uhttps://infoscience.epfl.ch/record/181974/files/v14n1a05.pdf$$yn/a$$zn/a
000181974 909C0 $$0252139$$pUPHESS$$xU10968
000181974 909CO $$ooai:infoscience.tind.io:181974$$pSV$$particle$$qGLOBAL_SET
000181974 917Z8 $$x105396
000181974 937__ $$aEPFL-ARTICLE-181974
000181974 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000181974 980__ $$aARTICLE