Higher fundamental functors for simplicial sets
Cahiers de Topologie et Géométrie Différentielle Catégoriques (2001)
- Volume: 42, Issue: 2, page 101-136
- ISSN: 1245-530X
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topGrandis, Marco. "Higher fundamental functors for simplicial sets." Cahiers de Topologie et Géométrie Différentielle Catégoriques 42.2 (2001): 101-136. <http://eudml.org/doc/91642>.
@article{Grandis2001,
author = {Grandis, Marco},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {adjoint functors; van Kampen theorem; symmetric simplicial set; fundamental groupoids; nerve; directed homotopy; simplicial sets},
language = {eng},
number = {2},
pages = {101-136},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Higher fundamental functors for simplicial sets},
url = {http://eudml.org/doc/91642},
volume = {42},
year = {2001},
}
TY - JOUR
AU - Grandis, Marco
TI - Higher fundamental functors for simplicial sets
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2001
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 42
IS - 2
SP - 101
EP - 136
LA - eng
KW - adjoint functors; van Kampen theorem; symmetric simplicial set; fundamental groupoids; nerve; directed homotopy; simplicial sets
UR - http://eudml.org/doc/91642
ER -
References
top- [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. Zbl1013.18003
- [2] J. Adamek - J. Rosicky, Locally presentable and accessible categories, Cambridge Univ. Press, Cambridge, 1994. Zbl0795.18007MR1294136
- [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. Zbl0912.18006MR1623672
- [4] R. Brown - P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra21 (1981), 233-260. Zbl0468.55007MR617135
- [5] R. Brown - P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra22 (1981), 11-41. Zbl0475.55009MR621285
- [6] R. Brown - P.J. Higgins, The equivalence of ∞-groupoids and crossed complexes, Cahiers Topologie Géom. Diff. Catég.22 (1981), 371-386. Zbl0487.55007
- [7] P. Freyd, Aspects of topoi, Bull. Austral. Math. Soc.7 (1972), 1-76. Zbl0252.18001MR396714
- [8] P. Gabriel - F. Ulmer, Lokal präsentierbare Kategorien, Lecture Notes in Mathematics221, Springer1971. Zbl0225.18004MR327863
- [9] M. Grandis, Cubical monads and their symmetries, in: Proc. of the Eleventh Intern. Conf. on Topology, Trieste1993, Rend. Ist. Mat. Univ. Trieste25 (1993), 223-262. Zbl0834.55012MR1346324
- [10] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures5 (1997), 363-413. Zbl0906.55015MR1478526
- [11] M. Grandis, An intrinsic homotopy theory for simplicial complexes, with applications to image analysis, Appl. Categ. Structures, to appear. Zbl0994.55011MR1891107
- [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. Structures8 (2000), 209-234. Zbl0966.55010MR1785844
- [15] K.A. Hardie - K.H. Kamps - R.W. Kieboom, A homotopy bigroupoid of a topological space, Appl. Categ. Structures, to appear. Zbl0987.18006
- [16] M. Johnson - R.F.C. Walters, On the nerve of an n-category, Cahiers Topologie Géom. Diff. Catég.28 (1987), 257-282. Zbl0662.18006MR926546
- [17] D.M. Kan, Adjoint functors, Trans. Amer. Math. Soc.87 (1958), 294-329. Zbl0090.38906MR131451
- [18] D.M. Kan, Functors involving c.s.s. complexes, Trans. Amer. Math. Soc.87 (1958), 330-346. Zbl0090.39001MR131873
- [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. Studies42 (1963), 28-46. Zbl0244.18008MR170925
- [21] S. Mac Lane, Categories for the working mathematician, Springer1971. Zbl0906.18001MR1712872
- [22] S. Mac Lane - I. Moerdijk, Sheaves in geometry and logic, Springer1992. Zbl0822.18001MR1300636
- [23] M. Makkai - R. Paré, Accessible categories: the foundations of categorical model theory, Contemp. Math.104, Amer. Math. Soc., Providence, RI, 1989. Zbl0703.03042MR1031717
- [24] J.P. May, Simplicial objects in algebraic topology, Van Nostrand1967. Zbl0165.26004MR222892
- [25] J.D. Stasheff, Homotopy associativity of H-spaces, I, Trans. Amer. Math. Soc.108 (1963), 275-292. Zbl0114.39402MR158400
- [26] J.D. Stasheff, Homotopy associativity of H-spaces, II, Trans. Amer. Math. Soc.108 (1963), 293-312. Zbl0114.39402MR158400
- [27] R. Street, The algebra of oriented simplexes, J. Pure Appl. Algebra49 (1987), 283-385. Zbl0661.18005MR920944
- [28] Z. Tamsamani, Equivalence de la théorie homotopique des n-groupoïdes et celle des espaces topologiques n-tronqués, Preprint.
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