Higher fundamental functors for simplicial sets
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001) no. 2, pp. 101-136. 
@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},
     pages = {101--136},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {42},
     number = {2},
     year = {2001},
     mrnumber = {1839359},
     zbl = {1006.18014},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_2001__42_2_101_0/}
}
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Grandis, Marco. Higher fundamental functors for simplicial sets. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001) no. 2, pp. 101-136. http://www.numdam.org/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

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

[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 | Zbl

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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

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

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

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