Higher fundamental functors for simplicial sets
Grandis, Marco
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001), p. 101-136 / Harvested from Numdam
@article{CTGDC_2001__42_2_101_0,
     author = {Grandis, Marco},
     title = {Higher fundamental functors for simplicial sets},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {42},
     year = {2001},
     pages = {101-136},
     mrnumber = {1839359},
     zbl = {1006.18014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2001__42_2_101_0}
}
Grandis, Marco. Higher fundamental functors for simplicial sets. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001) pp. 101-136. http://gdmltest.u-ga.fr/item/CTGDC_2001__42_2_101_0/

[1] F.A.A. Al-Agl - R. Brown - R. Steiner, Multiple categories: the equivalence of a globular and a cubical approach, at: http://arXiv.org/abs/math.CT/0007009. | Zbl 1013.18003

[2] J. Adamek - J. Rosicky, Locally presentable and accessible categories, Cambridge Univ. Press, Cambridge, 1994. | MR 1294136 | Zbl 0795.18007

[3] M.A. Batanin, Monoidal globular categories as a natural environment for the theory of weak n-categories, Adv. in Math. 136 (1997), 39-103. | MR 1623672 | Zbl 0912.18006

[4] R. Brown - P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260. | MR 617135 | Zbl 0468.55007

[5] R. Brown - P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981), 11-41. | MR 621285 | Zbl 0475.55009

[6] R. Brown - P.J. Higgins, The equivalence of ∞-groupoids and crossed complexes, Cahiers Topologie Géom. Diff. Catég. 22 (1981), 371-386. | Numdam | Zbl 0487.55007

[7] P. Freyd, Aspects of topoi, Bull. Austral. Math. Soc. 7 (1972), 1-76. | MR 396714 | Zbl 0252.18001

[8] P. Gabriel - F. Ulmer, Lokal präsentierbare Kategorien, Lecture Notes in Mathematics 221, Springer 1971. | MR 327863 | Zbl 0225.18004

[9] M. Grandis, Cubical monads and their symmetries, in: Proc. of the Eleventh Intern. Conf. on Topology, Trieste 1993, Rend. Ist. Mat. Univ. Trieste 25 (1993), 223-262. | MR 1346324 | Zbl 0834.55012

[10] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures 5 (1997), 363-413. | MR 1478526 | Zbl 0906.55015

[11] M. Grandis, An intrinsic homotopy theory for simplicial complexes, with applications to image analysis, Appl. Categ. Structures, to appear. | MR 1891107 | Zbl 0994.55011

[12] M. Grandis, Simplicial toposes and combinatorial homotopy, Dip. Mat. Univ. Genova, Preprint 400 (1999).

[13] A. Grothendieck, Pursuing stalks, unpublished manuscript, 1983.

[14] K.A. Hardie - K.H. Kamps - R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, Appl. Categ. Structures 8 (2000), 209-234. | MR 1785844 | Zbl 0966.55010

[15] K.A. Hardie - K.H. Kamps - R.W. Kieboom, A homotopy bigroupoid of a topological space, Appl. Categ. Structures, to appear. | Zbl 0987.18006

[16] M. Johnson - R.F.C. Walters, On the nerve of an n-category, Cahiers Topologie Géom. Diff. Catég. 28 (1987), 257-282. | Numdam | MR 926546 | Zbl 0662.18006

[17] D.M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329. | MR 131451 | Zbl 0090.38906

[18] D.M. Kan, Functors involving c.s.s. complexes, Trans. Amer. Math. Soc. 87 (1958), 330-346. | MR 131873 | Zbl 0090.39001

[19] F.W. Lawvere, Toposes generated by codiscrete objects, in combinatorial topology and functional analysis, Notes for Colloquium lectures given at North Ryde, NSW, Aus (1988), at Madison, Wisconsin, USA (1989), and at Seminario Matematico e Fisico, Milano, Italy (1992).

[20] Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 42 (1963), 28-46. | MR 170925 | Zbl 0244.18008

[21] S. Mac Lane, Categories for the working mathematician, Springer 1971. | MR 1712872 | Zbl 0906.18001

[22] S. Mac Lane - I. Moerdijk, Sheaves in geometry and logic, Springer 1992. | MR 1300636 | Zbl 0822.18001

[23] M. Makkai - R. Paré, Accessible categories: the foundations of categorical model theory, Contemp. Math. 104, Amer. Math. Soc., Providence, RI, 1989. | MR 1031717 | Zbl 0703.03042

[24] J.P. May, Simplicial objects in algebraic topology, Van Nostrand 1967. | MR 222892 | Zbl 0165.26004

[25] J.D. Stasheff, Homotopy associativity of H-spaces, I, Trans. Amer. Math. Soc. 108 (1963), 275-292. | MR 158400 | Zbl 0114.39402

[26] J.D. Stasheff, Homotopy associativity of H-spaces, II, Trans. Amer. Math. Soc. 108 (1963), 293-312. | MR 158400 | Zbl 0114.39402

[27] R. Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987), 283-385. | MR 920944 | Zbl 0661.18005

[28] Z. Tamsamani, Equivalence de la théorie homotopique des n-groupoïdes et celle des espaces topologiques n-tronqués, Preprint.