Essential properties of pro-objects in Grothendieck categories
Porter, Timothy
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 20 (1979), p. 3-57 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CTGDC_1979__20_1_3_0,
     author = {Porter, Timothy},
     title = {Essential properties of pro-objects in Grothendieck categories},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {20},
     year = {1979},
     pages = {3-57},
     mrnumber = {544528},
     zbl = {0414.18006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1979__20_1_3_0}
}

Porter, Timothy. Essential properties of pro-objects in Grothendieck categories. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 20 (1979) pp. 3-57. http://gdmltest.u-ga.fr/item/CTGDC_1979__20_1_3_0/

1 M. Artin and B. Mazur, Etale Homotopy, Lecture Notes in Math. 100, Springer (1969). | MR 245577 | Zbl 0182.26001

2 A. Deleanu and P. Hilton, Borsuk shape and Grothendieck categories of pro-objects, Math. Proc. Camb. Phil. Soc. 79-3 (1976), 473 - 482. | MR 400220 | Zbl 0327.18004

3 P. Deligne, Cohomologie à support propre et construction du foncteur f!, Appendix to Hartshorne: Residues and duality, Lecture Notes in Math. 20, Springer (1966). | MR 222093 | Zbl 0212.26101

4 M. Demazure and P. Gabriel, Groupes algébriques, Tome 1, Masson-North Holland, 1970. | Zbl 0203.23401

5 S.E. Dickson, A torsion theory for abelian categories, Trans. A.M.S. 121 (1966), 233- 235. | MR 191935 | Zbl 0138.01801

6 J. Duskin, Pro-objects ( after Verdier), Sém. Heidelberg- Strasbourg 1966 -67, Exposé 6, I.R.M.A. Strasbourg.

7 D. Edwards and H. Hastings, Čech and Steenrod homotopy theories, Lecture Notes in Math. 542, Springer (1976). | MR 428322 | Zbl 0334.55001

8 P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448 (Thèse, Paris, 1961). | Numdam | MR 232821 | Zbl 0201.35602

9 P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Erg. der Math. 35, Springer, 1967. | MR 210125 | Zbl 0186.56802

10 P. Gabriel and R. Rentschler, Sur la dimension des anneaux et ensembles ordonnés, C.R.A.S. Paris, Série A, 265 (1967), 712-715. | MR 224644 | Zbl 0155.36201

11 R. Gordon and J.C. Robson, Krull dimension, Mem. A. M. S. 133. | Zbl 0269.16017

12 R. Gordon and J.C. Robson, The Gabriel dimension of a module, J. Algebra 29 (1974), 459- 473. | MR 369425 | Zbl 0285.16018

13 A. Grothendieck, Techniques de descente et théorèmes d'existence en Géométrie algébrique, Sém. Bourbaki 195 (1960). | Numdam

14 L. Gruson and C.U. Jensen, Modules algébriquement compacts et foncteurs lim(i), C. R. A. S. Paris 276 (1973), 1651-1653. | MR 320112 | Zbl 0259.18015

15 L. Gruson and C.U. Jensen, Sur l'annulation de lim(i), Mat. Inst., Copenhagen University (1973).

16 M. Hacque, Eléments de la théorie de la localisation, Notes d'Enseignement (D.E.A.), Dépt. Math., Univ. Lyon, 1 (1970).

17 M. Hacque, Caractérisations générales des localisations, Publi. Dept. Math. Lyon 7-4 (1970), 45-103. | MR 347904 | Zbl 0253.18011

18 A.G. Heinicke, Triples and localisations, Canad. Math. Bull. 14-3 (1971), 333- 339. | MR 318229 | Zbl 0218.16015

19 P. Hilton and U. Stammbach, A course in homological Algebra, Graduate Texts in Math. 4, Springer, 1970. | MR 1438546 | Zbl 0863.18001

20 C.U. Jensen, On the vanishing of lim(i), J. Algebra 15-2 (1970), 151-166. | MR 260839 | Zbl 0199.36202

21 C.U. Jensen, Les foncteurs dérivés de lim et leurs applications en Théorie des modules, Lecture Notes in Math. 254, Springer (1972). | MR 407091 | Zbl 0238.18007

22 J.L. Ambek, Torsion theories, additive semantics and rings of quotients, Lecture Note s in Math. 177, Springer (1971). | MR 284459 | Zbl 0213.31601

23 O.A. Laudal, Sur la limite projective et la théorie de la dimension, Topo. et Géo. Diff. V (1961). | Numdam | Zbl 0192.11001

24 S. Maclane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer, 1970. | MR 1712872 | Zbl 0705.18001

25 U. Oberst, Duality theory for Grothendieck categories and linearly compact rings, J. Algebra 15 (1970), 473-542. | MR 447371 | Zbl 0274.18011

26 N. Popescu, Abelian categories with applications to rings and modules, London Math. Soc. Monographs 3, Academic Press, 1973. | MR 340375 | Zbl 0271.18006

27 T. Porter, Abstract homotopy theory in procategories, Cahiers Topo. et Géo. Diff. XVII- 2 (1976), 113-125. | Numdam | MR 445496 | Zbl 0349.18012

28 T. Porter, Coherent prohomotopy theory, Idem XIX- 1 (1978), 3-46. | Numdam | MR 496541 | Zbl 0387.55013

29 T. Porter, Coherent prohomotopical algebra, Idem XVIII- 2 (1977), 139-180. | Numdam | MR 470033 | Zbl 0364.18009

30 T. Porter, Stability of algebraic inverse systems, I: Stability, Weak stability and the weakly stable socle, Fund. Math. 100 (1978), 17. | MR 497750 | Zbl 0399.18004

31 T. Porter, Stability of algebraic inverse systems, II: Purity and localisation, J. Pure and Appl. Algebra 7 (1976), 133- 143. | MR 411525 | Zbl 0325.18009

32 T. Porter, Stability results for algebraic inverse systems, Proc. Royal Irish Acad, Section A, 76-9 (1976), 79-83. | MR 424898 | Zbl 0334.18020

33 T. Porter, Torsion theoretic results in procategories I, II, III, Proc. Royal Irish Acad. 76 A (1976), 145- 172. | MR 427423 | Zbl 0355.18014

34 T. Porter, Quelques résultats sur les anneaux semi-noethériens, Bull. Acad. Polon. Sci. 25 (1976), 829-834. | MR 427373 | Zbl 0341.16014

35 D. Quillen, Homotopical Algebra, Lecture Notes in Math. 43 (1967). | MR 223432 | Zbl 0168.20903

36 J.E. Roos, Bidualité et structure des foncteurs dérivés de lim dans la catégorie des modules sur un anneau régulier, C.R.A.S. Paris 254 (1962). | MR 136640 | Zbl 0109.25203

37 H.B. Stauffer, A relationship between left exact and representable functors, Can. J. Math. 23 - 2 (1971), 374- 380. | MR 271189 | Zbl 0218.18008

38 H.B. Stauffer, Completions of abelian categories, Trans. A. M. S. 170. | Zbl 0267.18004

39 B. Stenström, Rings and modules of quotients, Lecture Notes in Math. 237. | Zbl 0229.16003

40 J.-L. Verdier, Equivalence essentielle des systèmes projectifs, C. R.A.S. Paris 261 (1965), 4950 - 4953. | MR 190209 | Zbl 0135.02203