Modules over Operads and Functors (eBook)

Benoit Fresse (Autor)

eBook Download: PDF

2009 | 2009
X, 314 Seiten
Springer Berlin (Verlag)
978-3-540-89056-0 (ISBN)

Infos

This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Inhalt

Categorical 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.

Produkt-Details

• Erscheint lt. Verlag: 20.4.2009
• Reihe/Serie: Lecture Notes in Mathematics
• Verlagsort: Berlin
• Sprache: englisch
• Schlagworte: 18D50, 55P48, 18G55, 18A25 • Algebraic Structure • algebraic topology • Cohomology theory • Homology • Homotopy • Model Category • Operad • Symmetric Monoidal Category
• ISBN-10: 3-540-89056-4 / 3540890564
• ISBN-13: 978-3-540-89056-0 / 9783540890560