Iterated monoidal categories

Autor(en): Balteanu, C
Fiedorowicz, Z
Schwanzl, R
Vogt, R
Stichwörter: braided monoidal category; coherence theory; E-n-space; iterated loop space; LOOP-SPACES; Mathematics; Milgram model for Omega(n)Sigma X-n; operad; OPERADS; preoperad; Smith filtration; symmetric monoidal category
Erscheinungsdatum: 2003
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 176
Ausgabe: 2
Startseite: 277
Seitenende: 349
Zusammenfassung: 
We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for Omega(2)Sigma(2)X when n = 2 and is very closely related to Milgram's model of Omega(n)Sigma(n)X for n>2. (C) 2003 Elsevier Science (USA). All rights reserved.
ISSN: 00018708
DOI: 10.1016/S0001-8708(03)00065-3

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