Grandis, Marco
On the categorical foundations of homological and homotopical algebra
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 33 (1992) no. 2 , p. 135-175
Zbl 0814.18006 | MR 1168336 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=CTGDC_1992__33_2_135_0

Bibliographie

[An] D.W. Anderson, Axiomatic homotopy theory, in: Algebraic Topology, Waterloo, 1978, p. 520-547, Lect. Notes in Math. 741, Springer 1979. MR 557184 | Zbl 0438.55010

[Ba] H.J. Baues, Algebraic homotopy, Cambridge Univ. Press 1989. MR 985099 | Zbl 0688.55001

[BK] A.K. Bousfield - D.M. Kan, Homotopy limits, completions and localizations, Lect. Notes in Math. 304, Springer 1972. MR 365573 | Zbl 0259.55004

[Br] K.S. Brown, Abstract homotopy theory and generalised sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973), 419-458. MR 341469 | Zbl 0245.55007

[Bu] D.A. Buchsbaum, Exact categories and duality, Trans. Amer. Math. Soc. 80 (1955), 1-34. MR 74407 | Zbl 0065.25502

[CE] H. Cartan - S. Eilenberg, Homological algebra, Princeton Univ. Press 1956. MR 77480 | Zbl 0075.24305

[DT] A. Dold - R. Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958), 239-281. MR 97062 | Zbl 0091.37102

[Eh] C. Ehresmann, Cohomologie à valeurs dans une catégorie dominée, Extraits du Colloque de Topologie, Bruxelles 1964, in: C. Ehresmann, Oeuvres complètes et commentées, Partie III-2, 531-590, Amiens 1980 (8). Zbl 0201.35502

[ES] S. Eilenberg - N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press 1952. MR 50886 | Zbl 0047.41402

[G1] M. Grandis, Symétrisations de categories et catégories quaternaires, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. 14 sez. 1 (1977), 133-207. MR 472959 | Zbl 0418.18003

[G2] M. Grandis, On distributive homological algebra, I-III. Cahiers Top. Géom. Diff. 25 (1984), 259-301; 353-379; 26 (1985), 169-213. Numdam | Zbl 0564.18005

[G3] M. Grandis, A categorical approach to exactness in algebraic topology, in: Atti del V Convegno Intemazionale di Topologia, Lecce-Otranto 1990, Rend. Circ. Mat. Palermo, to appear. MR 1197170 | Zbl 0770.55013

[G4] M. Grandis, On homological algebra, I. Semiexact and homological categories, Dip. Mat. Univ. Genova, Preprint 186 (1991), 1-45 (9).

[G5] M. Grandis, On homological algebra, II. Homology and satellites, Dip. Mat. Univ. Genova, Preprint 187 (1991), 1-39.

[G6] M. Grandis, Homotopical algebra: a two-dimensional categorical setting, Dip. Mat. Univ. Genova, Preprint 191 (1991), 1-50.

[Ga] P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-348. Numdam | MR 232821 | Zbl 0201.35602

[Gr] A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957), 119-221. MR 102537 | Zbl 0118.26104

[GV1] A.R. Grandjeán - L. Valcárcel, Homología en categorías exactas, Dep. de Algebra y Fundamentos, Santiago de Compostela, 1970. MR 285586 | Zbl 0291.18014

[GV2] A.R. Grandjeán - L. Valcárcel, Pares exactos y sucesiones espectrales, ibidem, 1974.

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

[H1] A. Heller, Stable homotopy categories, Bull. Amer. Math. Soc. 74 (1968), 28-63. MR 224090 | Zbl 0177.25605

[H2] A. Heller, Homotopy theories, Mem. Amer. Math. Soc. 383 (1988). MR 920963 | Zbl 0643.55015

[Hb1] P.J. Huber, Homotopy theories in general categories, Math. Ann. 144 (1961), 361-385. MR 150184 | Zbl 0099.17905

[Hb2] P.J. Huber, Standard constructions in abelian categories, Math. Ann. 146 (1962), 321-325. MR 150185 | Zbl 0101.40701

[K1] K.H. Kamps, Über einige formale Eigenschaften von Faserungen und h-Faserungen, Manuscripta Math. 3 (1970), 237-255. MR 270374 | Zbl 0205.27502

[K2] K.H. Kamps, Zur Homotopietheorie von Gruppoiden, Arch. Math.(Basel) 23 (1972), 610-618. MR 315022 | Zbl 0251.20059

[Ka] D.M. Kan, Abstract homotopy I-IV, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 1092-1096; 42 (1956), 255-258; 419-421; 542-544. MR 79762 | Zbl 0065.38601

[Ke] G.M. Kelly, Single-space axioms for homology theories, Proc. Cambridge Philos. Soc. 55 (1959), 10-22. MR 108787 | Zbl 0084.19001

[Ks] H. Kleisli, Homotopy theory in abelian categories, Canad. J. Math. 14 (1962), 139-169. MR 141696 | Zbl 0108.02001

[La] R. Lavendhomme, Un plongement pleinement fidèle de la catégorie des groupes, Bull. Soc. Math. Belgique, 17 (1965), 153-185. MR 186713 | Zbl 0146.02602

[LV] R. Lavendhomme - G. Van Den Bossche, Homologisation de catégories prerégulières, Inst. de Math. Pure Appl., Univ. Catholique de Louvain 41 (1973), 1-24.

[Ma] S. Mac Lane, Homology, Springer, 1963. MR 1344215 | Zbl 0818.18001

[Mc] H.J. Marcum, Homotopy equivalences in 2-categories, in: Groups of self-equivalences and related topics, Montréal 1988, p. 71-86, Lect. Notes in Math. 1425, Springer 1990. MR 1070577 | Zbl 0712.55006

[Mh] M. Mather, Pull-backs in homotopy theory, Can. J. Math. 28 (1976), 225-263. [Mt] B. Mitchell, Theory of categories, Academic Press 1965. MR 402694 | Zbl 0351.55005

[P1] D. Puppe, Homotopiemengen und ihre induzierten Abbildungen, I, Math. Z. 69 (1958), 299-344. MR 100265 | Zbl 0092.39803

[P2] D. Puppe, Korrespondenzen in abelschen Kategorien, Math. Ann. 148 (1962), 1-30. MR 141698 | Zbl 0109.25201

[Qn] D.G. Quillen, Homotopical algebra, Lect. Notes in Math. 43, Springer 1967. [Ze] E.C. Zeeman, On the filtered differential group, Ann. Math. 66 (1957), 557-585. MR 223432 | Zbl 0168.20903