Geodesic
Lax Operad Actions and Coherence for Monoidal n-Categories, A_{\infty} Rings and Modules
Theory and applications of categories, Tome 3 (1997), pp. 50-84

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We establish a general coherence theorem for lax operad actions on an n-category which implies that an n-category with such an action is lax equivalent to one with a strict action. This includes familiar coherence results (e.g. for symmetric monoidal categories) and many new ones. In particular, any braided monoidal n-category is lax equivalent to a strict braided monoidal n-category. We also obtain coherence theorems for A_{\infty} and E_{\infty} rings and for lax modules over such rings. Using these results we give an extension of Morita equivalence to A_{\infty} rings and some applications to infinite loop spaces and algebraic K-theory.

Classification : 18C15, 18D05, 18D10, 19D23, 55P47, 55U40.
Keywords: braided monoidal n-category, operad, ring spectrum, A8 ring, Morita equivalence. 
@article{TAC_1997_3_a3,
     author = {Gerald Dunn},
     title = {Lax {Operad} {Actions} and {Coherence} for {Monoidal} {
n-Categories,} {A_{\infty}} {Rings} 
and {Modules}},
     journal = {Theory and applications of categories},
     pages = {50--84},
     publisher = {mathdoc},
     volume = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1997_3_a3/}
}
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Gerald Dunn. Lax Operad Actions and Coherence for Monoidal 
n-Categories, A_{\infty} Rings 
and Modules. Theory and applications of categories, Tome 3 (1997), pp. 50-84. http://geodesic.mathdoc.fr/item/TAC_1997_3_a3/