A model structure on categories related to categories of complexes

  • V. V. Lyubashenko Institute of Mathematics, NAS of Ukraine
Keywords: model category, differential graded module, graded commutative ring

Abstract

UDC 512.58

We prove a Hinich-type theorem on the existence of a model structure on a category related by adjunction to the category of differential graded modules over a graded commutative ring.

References

Berger, Clemens; Moerdijk, Ieke. Axiomatic homotopy theory for operads. Comment. Math. Helv. 78 (2003), no. 4, 805--831. doi: 10.1007/s00014-003-0772-y

Christensen, J. Daniel; Hovey, Mark. Quillen model structures for relative homological algebra. Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 2, 261--293. doi: 10.1017/S0305004102006126

Harper, John E. Homotopy theory of modules over operads and non-$Sigma$ operads in monoidal model categories. J. Pure Appl. Algebra 214 (2010), no. 8, 1407--1434. doi: 10.1016/j.jpaa.2009.11.006

Hinich, Vladimir. Homological algebra of homotopy algebras. Comm. Algebra 25 (1997), no. 10, 3291--3323. doi: 10.1080/00927879708826055

Lyubashenko, Volodymyr. Homotopy unital $A_infty$-algebras. J. Algebra 329 (2011), 190--212. doi: 10.1016/j.jalgebra.2010.02.009

Lyubashenko, Volodymyr. Homotopy unital $A_infty$-morphisms with several entries. Theory Appl. Categ. 30 (2015), Paper No. 46, 1552--1623. MR3421459

Muro, Fernando. Homotopy theory of nonsymmetric operads. Algebr. Geom. Topol. 11 (2011), no. 3, 1541--1599. doi: 10.2140/agt.2011.11.1541

M. Spitzweck, Operads, algebras and modules in general model categories, jan 2001, arXiv: math/ 0101102.

Schwede, Stefan; Shipley, Brooke E. Algebras and modules in monoidal model categories. Proc. London Math. Soc. (3) 80 (2000), no. 2, 491--511. doi: 10.1112/S002461150001220X

Published
15.02.2020
How to Cite
Lyubashenko, V. V. “A Model Structure on Categories Related to Categories of Complexes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 2, Feb. 2020, pp. 232-44, http://umj.imath.kiev.ua/index.php/umj/article/view/682.
Section
Research articles