caa a22 4500 445378638 CHVBK 20180317143010.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-008-9179-7 doi (NATIONALLICENCE)springer-10.1007/s10485-008-9179-7 Algebras of Higher Operads as Enriched Categories [Elektronische Daten] [Michael Batanin, Mark Weber] One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads (Batanin, Adv Math 136:39-103, 1998) to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following the idea that a weak (n + 1)-category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads. Springer Science+Business Media B.V., 2008 Operads nationallicence Higher dimensional categories nationallicence Lax monoidal categories nationallicence Enriched categories nationallicence Batanin Michael Department of Mathematics, Macquarie University, Sydney, Australia aut Weber Mark Laboratoire PPS, Université Paris Diderot, Paris 7, France aut Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 93-135 0927-2852 19:1<93 2011 19 10485 https://doi.org/10.1007/s10485-008-9179-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-008-9179-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Batanin Michael Department of Mathematics, Macquarie University, Sydney, Australia aut NATIONALLICENCE 700 1- Weber Mark Laboratoire PPS, Université Paris Diderot, Paris 7, France aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 93-135 0927-2852 19:1<93 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer