000 03490nam a22004815i 4500
001 978-3-540-89056-0
003 DE-He213
005 20190213151725.0
007 cr nn 008mamaa
008 100301s2009 gw | s |||| 0|eng d
020 _a9783540890560
_9978-3-540-89056-0
024 7 _a10.1007/978-3-540-89056-0
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aFresse, Benoit.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aModules over Operads and Functors
_h[electronic resource] /
_cby Benoit Fresse.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aX, 314 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1967
505 0 _aCategorical and operadic background -- Symmetric monoidal categories for operads -- Symmetric objects and functors -- Operads and algebras in symmetric monoidal categories -- Miscellaneous structures associated to algebras over operads -- The category of right modules over operads and functors -- Definitions and basic constructions -- Tensor products -- Universal constructions on right modules over operads -- Adjunction and embedding properties -- Algebras in right modules over operads -- Miscellaneous examples -- Homotopical background -- Symmetric monoidal model categories for operads -- The homotopy of algebras over operads -- The (co)homology of algebras over operads -- The homotopy of modules over operads and functors -- The model category of right modules -- Modules and homotopy invariance of functors -- Extension and restriction functors and model structures -- Miscellaneous applications -- Appendix: technical verifications -- Shifted modules over operads and functors -- Shifted functors and pushout-products -- Applications of pushout-products of shifted functors.
520 _aThe notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.
650 0 _aAlgebra.
650 0 _aAlgebraic topology.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aCategory Theory, Homological Algebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11035
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540891468
776 0 8 _iPrinted edition:
_z9783540890553
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1967
856 4 0 _uhttps://doi.org/10.1007/978-3-540-89056-0
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11661
_d11661