@article{CTGDC_1992__33_2_135_0, author = {Grandis, Marco}, title = {On the categorical foundations of homological and homotopical algebra}, journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, volume = {33}, year = {1992}, pages = {135-175}, mrnumber = {1168336}, zbl = {0814.18006}, language = {en}, url = {http://dml.mathdoc.fr/item/CTGDC_1992__33_2_135_0} }
Grandis, Marco. On the categorical foundations of homological and homotopical algebra. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 33 (1992) pp. 135-175. http://gdmltest.u-ga.fr/item/CTGDC_1992__33_2_135_0/
[An] Axiomatic homotopy theory, in: Algebraic Topology, Waterloo, 1978, p. 520-547, Lect. Notes in Math. 741, Springer 1979. | MR 557184 | Zbl 0438.55010
,[Ba] Algebraic homotopy, Cambridge Univ. Press 1989. | MR 985099 | Zbl 0688.55001
,[BK] Homotopy limits, completions and localizations, Lect. Notes in Math. 304, Springer 1972. | MR 365573 | Zbl 0259.55004
- ,[Br] Abstract homotopy theory and generalised sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973), 419-458. | MR 341469 | Zbl 0245.55007
,[Bu] Exact categories and duality, Trans. Amer. Math. Soc. 80 (1955), 1-34. | MR 74407 | Zbl 0065.25502
,[CE] Homological algebra, Princeton Univ. Press 1956. | MR 77480 | Zbl 0075.24305
- ,[DT] Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958), 239-281. | MR 97062 | Zbl 0091.37102
- ,[Eh] 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] Foundations of algebraic topology, Princeton Univ. Press 1952. | MR 50886 | Zbl 0047.41402
- ,[G1] 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] 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] 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] On homological algebra, I. Semiexact and homological categories, Dip. Mat. Univ. Genova, Preprint 186 (1991), 1-45 (9).
,[G5] On homological algebra, II. Homology and satellites, Dip. Mat. Univ. Genova, Preprint 187 (1991), 1-39.
,[G6] Homotopical algebra: a two-dimensional categorical setting, Dip. Mat. Univ. Genova, Preprint 191 (1991), 1-50.
,[Ga] Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-348. | Numdam | MR 232821 | Zbl 0201.35602
,[Gr] Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957), 119-221. | MR 102537 | Zbl 0118.26104
,[GV1] Homología en categorías exactas, Dep. de Algebra y Fundamentos, Santiago de Compostela, 1970. | MR 285586 | Zbl 0291.18014
- ,[GV2] Pares exactos y sucesiones espectrales, ibidem, 1974.
- ,[GZ] Calculus of fractions and homotopy theory, Springer 1967. | MR 210125 | Zbl 0186.56802
- ,[H1] Stable homotopy categories, Bull. Amer. Math. Soc. 74 (1968), 28-63. | MR 224090 | Zbl 0177.25605
,[H2] Homotopy theories, Mem. Amer. Math. Soc. 383 (1988). | MR 920963 | Zbl 0643.55015
,[Hb1] Homotopy theories in general categories, Math. Ann. 144 (1961), 361-385. | MR 150184 | Zbl 0099.17905
,[Hb2] Standard constructions in abelian categories, Math. Ann. 146 (1962), 321-325. | MR 150185 | Zbl 0101.40701
,[K1] Über einige formale Eigenschaften von Faserungen und h-Faserungen, Manuscripta Math. 3 (1970), 237-255. | MR 270374 | Zbl 0205.27502
,[K2] Zur Homotopietheorie von Gruppoiden, Arch. Math.(Basel) 23 (1972), 610-618. | MR 315022 | Zbl 0251.20059
,[Ka] 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] Single-space axioms for homology theories, Proc. Cambridge Philos. Soc. 55 (1959), 10-22. | MR 108787 | Zbl 0084.19001
,[Ks] Homotopy theory in abelian categories, Canad. J. Math. 14 (1962), 139-169. | MR 141696 | Zbl 0108.02001
,[La] Un plongement pleinement fidèle de la catégorie des groupes, Bull. Soc. Math. Belgique, 17 (1965), 153-185. | MR 186713 | Zbl 0146.02602
,[LV] Homologisation de catégories prerégulières, Inst. de Math. Pure Appl., Univ. Catholique de Louvain 41 (1973), 1-24.
- ,[Ma] Homology, Springer, 1963. | MR 1344215 | Zbl 0818.18001
,[Mc] 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] Pull-backs in homotopy theory, Can. J. Math. 28 (1976), 225-263. [Mt] , Theory of categories, Academic Press 1965. | MR 402694 | Zbl 0351.55005
,[P1] Homotopiemengen und ihre induzierten Abbildungen, I, Math. Z. 69 (1958), 299-344. | MR 100265 | Zbl 0092.39803
,[P2] Korrespondenzen in abelschen Kategorien, Math. Ann. 148 (1962), 1-30. | MR 141698 | Zbl 0109.25201
,[Qn] Homotopical algebra, Lect. Notes in Math. 43, Springer 1967. [Ze] , On the filtered differential group, Ann. Math. 66 (1957), 557-585. | MR 223432 | Zbl 0168.20903
,