Weak subobjects and weak limits in categories and homotopy categories
Grandis, Marco
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997), p. 301-326 / Harvested from Numdam
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Publié le : 1997-01-01
@article{CTGDC_1997__38_4_301_0,
     author = {Grandis, Marco},
     title = {Weak subobjects and weak limits in categories and homotopy categories},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {38},
     year = {1997},
     pages = {301-326},
     mrnumber = {1487963},
     zbl = {0891.18001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1997__38_4_301_0}
}

Grandis, Marco. Weak subobjects and weak limits in categories and homotopy categories. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) pp. 301-326. http://gdmltest.u-ga.fr/item/CTGDC_1997__38_4_301_0/

[1] M. Barr - C.F. Wells, Toposes, triples and theories, Springer 1984. | MR 771116 | Zbl 0567.18001

[2] H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, de Gruyter, Berlin 1991. | MR 1096295 | Zbl 0716.55001

[3] H.J. Baues, Homotopy type and homology, Oxford Science Publ, Clarendon Press, Oxford 1996. | MR 1404516 | Zbl 0857.55001

[4] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Coll. Publ. 25, New York 1948. | MR 29876 | Zbl 0033.10103

[5] A.K. Bousfield - D.M. Kan, Homotopy limits, completions and localisations, Lecture Notes in Mathematics 304, Springer 1972. | MR 365573 | Zbl 0259.55004

[6] A. Carboni - M. Grandis, Categories of projective spaces, J. Pure Appl. Algebra 110 (1996) 241-258. | MR 1393115 | Zbl 0863.18006

[7] A. Carboni - E. Vitale, Regular and exact completions, to appear. | MR 1600009 | Zbl 0891.18002

[8] L. Coppey, Algèbres de décompositions et précatégories, Diagrammes 3 (1980, supplément). | MR 684912 | Zbl 0497.18015

[9] B. Eckmann - P.J. Hilton, Unions and intersections in homotopy theory, Comm. Math. Helv. 38 (1963-64), 293-307. | MR 167982 | Zbl 0126.38903

[10] P. Freyd, Representations in abelian categories, in: Proceedings of the Conference on Categorical Algebra, La Jolla 1965, 95-120, Springer 1966. | MR 209333 | Zbl 0202.32402

[11] P. Freyd, Stable homotopy, in: Proceedings of the Conference on Categorical Algebra, La Jolla 1965, 121-176, Springer 1966. | MR 211399 | Zbl 0195.52901

[12] P. Freyd, Stable homotopy II, in: Proc. Symp. Pure Maths. XVII, Amer. Math. Soc. 1970, 161-183. | MR 258028 | Zbl 0222.55020

[13] P. Freyd, On the concreteness of certain categories, in: Symposia Mathematica, Vol. IV (INDAM, Roma 1968/69), pp. 431-456. Academic Press, London, 1970. | MR 271184 | Zbl 0248.18008

[14] P. Freyd, Homotopy is not concrete, in: The Steenrod algebra and its applications (Battelle Memorial Inst., Columbus, Ohio, 1970), pp. 25-34, Lecture Notes in Mathematics 168, Springer 1970. | MR 276961 | Zbl 0212.55801

[15] P. Gabriel - M. Zisman, Calculus of fractions and homotopy theory, Springer 1967. | MR 210125 | Zbl 0186.56802

[16] M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ. Structures, 2 (1994), 351-406. | MR 1300721 | Zbl 0826.55015

[17] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categorical Structures, to appear. | MR 1478526 | Zbl 0906.55015

[18] R.W. Kieboom, On stable homotopy monomorphisms, Appl. Categorical Structures, to appear. | MR 1456520 | Zbl 0873.18001

[19] M. Korostenski - W. Tholen, Factorisation systems as Eilenberg-Moore algebras, J. Pure Appl. Algebra 85 (1993), 57-72. | MR 1207068 | Zbl 0778.18001

[20] A.G. Kurosh, The theory of groups, Chelsea Publ. Co., New York 1960. | MR 109842 | Zbl 0064.25104

[21] F.W. Lawvere, Adjoints in and among bicategories, in: "Logic and Algebra", 181-189, M. Dekker, New York, 1996. | MR 1404939 | Zbl 0862.18002

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

[23] M. Mather, Pull-backs in homotopy theory, Can. J. Math. 28 (1976), 225-263. | MR 402694 | Zbl 0351.55005

[24] R.M. Vogt, Homotopy limits and colimits, Math. Z. 134 (1973), 11-52. | MR 331376 | Zbl 0276.55006

[25] G.W. Whitehead, Elements of homotopy theory, Springer 1978. | MR 516508 | Zbl 0406.55001