Associahedra and weak monoidal structures on categories
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 469-492
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

This paper answers the following question: what algebraic structure on a category corresponds to an An structure (in the sense of Stasheff) on the geometric realization of its nerve?

DOI : 10.2140/agt.2012.12.469
Keywords: associahedra, monoidal category, operad, Tamari lattice

Fiedorowicz, Zbigniew  1   ; Gubkin, Steven  1   ; Vogt, Rainer M  2

1 Department of Mathematics, Ohio State University, Columbus OH 43210-1174, USA
2 Fachbereich Mathematik/Informatik, Universität Osnabrück, Albrechtstr. 28a, D-49069 Osnabrück, Germany
@article{10_2140_agt_2012_12_469,
     author = {Fiedorowicz, Zbigniew and Gubkin, Steven and Vogt, Rainer~M},
     title = {Associahedra and weak monoidal structures on categories},
     journal = {Algebraic and Geometric Topology},
     pages = {469--492},
     year = {2012},
     volume = {12},
     number = {1},
     doi = {10.2140/agt.2012.12.469},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.469/}
}
TY  - JOUR
AU  - Fiedorowicz, Zbigniew
AU  - Gubkin, Steven
AU  - Vogt, Rainer M
TI  - Associahedra and weak monoidal structures on categories
JO  - Algebraic and Geometric Topology
PY  - 2012
SP  - 469
EP  - 492
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.469/
DO  - 10.2140/agt.2012.12.469
ID  - 10_2140_agt_2012_12_469
ER  - 
%0 Journal Article
%A Fiedorowicz, Zbigniew
%A Gubkin, Steven
%A Vogt, Rainer M
%T Associahedra and weak monoidal structures on categories
%J Algebraic and Geometric Topology
%D 2012
%P 469-492
%V 12
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.469/
%R 10.2140/agt.2012.12.469
%F 10_2140_agt_2012_12_469
Fiedorowicz, Zbigniew; Gubkin, Steven; Vogt, Rainer M. Associahedra and weak monoidal structures on categories. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 469-492. doi: 10.2140/agt.2012.12.469

[1] C Balteanu, Z Fiedorowicz, R Schwänzl, R M Vogt, Iterated monoidal categories, Adv. Math. 176 (2003) 277

[2] J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973)

[3] Z Fiedorowicz, S Gubkin, R M Vogt, Associahedra and weak monoidal structures on categories

[4] V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203

[5] A Joyal, R Street, Braided tensor categories, Adv. Math. 102 (1993) 20

[6] B Keller, Introduction to A–infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1

[7] M L Laplaza, Coherence for associativity not an isomorphism, J. Pure Appl. Algebra 2 (1972) 107

[8] T Leinster, Higher operads, higher categories, 298, Cambridge Univ. Press (2004)

[9] S Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 49 (1963) 28

[10] J P May, Definitions: operads, algebras and modules, from: "Operads : Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995)" (editors J L Loday, J D Stasheff, A A Voronov), Contemp. Math. 202, Amer. Math. Soc. (1997) 1

[11] D Quillen, Higher algebraic K–theory. I, from: "Algebraic K–theory, I : Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, WA, 1972)" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85

[12] J D Stasheff, Homotopy associativity of H–spaces. I, II, Trans. Amer. Math. Soc. 108 (1963) 275, 293

[13] J D Stasheff, The pre-history of operads, from: "Operads : Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995)" (editors J L Loday, J D Stasheff, A A Voronov), Contemp. Math., Amer. Math. Soc. (1997) 9

[14] J D Stasheff, How I “met” Dov Tamari, from: "Associahedra, Tamari Lattices and Related Structures Associahedra, Tamari Lattices and Related Structures" (editors F Müller-Hoissen, J M Pallo, J Stasheff), Progress in Math. 299, Springer (2012)

[15] D Tamari, Monoïdes préordonnés et chaînes de Malcev, PhD thesis, Université de Paris (1951)

[16] D Tamari, The algebra of bracketings and their enumeration, Nieuw Arch. Wisk. 10 (1962) 131

[17] Wikipedia, Tamari lattice, Wikipedia, The Free Encyclopedia (2012)

Cité par Sources :