Combinatoric n-fold categories and n-fold operads Export

@misc{citeulike:164592, abstract = {Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the associativity that must be a property of the action of an operad on any of its algebras. After a review of the role of operads in loop space theory and higher categories we go over definitions of iterated monoidal categories and introduce a large family of simple examples. Then we generalize the definition of operad by defining n-fold operads and their algebras in an iterated monoidal category. We discuss examples of these that live in the previously described categories. Finally we describe the (n-2)-fold monoidal category of n-fold V-operads.}, archivePrefix = {arXiv}, author = {Forcey, S. and Siehler, J.}, citeulike-article-id = {164592}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0411561}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0411561}, eprint = {math/0411561}, keywords = {iterated\_monoidal}, month = {November}, posted-at = {2006-09-18 13:33:58}, priority = {3}, title = {Combinatoric n-fold categories and n-fold operads}, url = {http://arxiv.org/abs/math/0411561}, year = {2004} }

TY - ELEC ID - citeulike:164592 L3 - citeulike-article-id:164592 N2 - Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the associativity that must be a property of the action of an operad on any of its algebras. After a review of the role of operads in loop space theory and higher categories we go over definitions of iterated monoidal categories and introduce a large family of simple examples. Then we generalize the definition of operad by defining n-fold operads and their algebras in an iterated monoidal category. We discuss examples of these that live in the previously described categories. Finally we describe the (n-2)-fold monoidal category of n-fold V-operads. TI - Combinatoric n-fold categories and n-fold operads KW - iterated_monoidal AU - Forcey, S AU - Siehler, J PY - 2004/11/25/ UR - http://arxiv.org/abs/math/0411561 ER -