000150239 001__ 150239
000150239 005__ 20190726102159.0
000150239 02470 $$a1007.1934$$2arXiv
000150239 037__ $$aARTICLE
000150239 245__ $$aTwisting structures and strongly homotopy morphisms
000150239 269__ $$a2010
000150239 260__ $$c2010
000150239 336__ $$aJournal Articles
000150239 520__ $$aIn an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad and let BP be the bar construction on the operad P. To each morphism of cooperads g from Q to BP is associated a P-co-ring, K(g), which generalizes the two-sided Koszul and bar constructions. When the co-unit from K(g) to P is a quasi-isomorphism, we show that the Kleisli category for K(g) is isomorphic to the category of P-algebras and of their morphisms up to strong homotopy, and we give the classifying morphisms for both strict and homotopy P-algebras. Parametrized morphisms of (co)associative chain (co)algebras up to strong homotopy are also introduced and studied, and a general existence theorem is proved. In the appendix, we study the particular case of the two-sided Koszul resolution of the associative operad.
000150239 700__ $$0240499$$g105396$$aHess, Kathryn
000150239 700__ $$aScott, Jonathan
000150239 773__ $$tArXiv
000150239 909C0 $$xU10968$$0252139$$pUPHESS
000150239 909CO $$qGLOBAL_SET$$pSV$$particle$$ooai:infoscience.tind.io:150239
000150239 917Z8 $$x139598
000150239 937__ $$aEPFL-ARTICLE-150239
000150239 973__ $$rNON-REVIEWED$$sSUBMITTED$$aEPFL
000150239 980__ $$aARTICLE