Geodesic
Numerical Invariants in Homotopical Algebra, I
Canadian journal of mathematics, Tome 27 (1975) no. 4, pp. 901-934

Voir la notice de l'article provenant de la source Cambridge University Press

Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated. 
Varadarajan, K. Numerical Invariants in Homotopical Algebra, I. Canadian journal of mathematics, Tome 27 (1975) no. 4, pp. 901-934. doi: 10.4153/CJM-1975-097-5
@article{10_4153_CJM_1975_097_5,
     author = {Varadarajan, K.},
     title = {Numerical {Invariants} in {Homotopical} {Algebra,} {I}},
     journal = {Canadian journal of mathematics},
     pages = {901--934},
     year = {1975},
     volume = {27},
     number = {4},
     doi = {10.4153/CJM-1975-097-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-097-5/}
}
TY  - JOUR
AU  - Varadarajan, K.
TI  - Numerical Invariants in Homotopical Algebra, I
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 901
EP  - 934
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-097-5/
DO  - 10.4153/CJM-1975-097-5
ID  - 10_4153_CJM_1975_097_5
ER  - 
%0 Journal Article
%A Varadarajan, K.
%T Numerical Invariants in Homotopical Algebra, I
%J Canadian journal of mathematics
%D 1975
%P 901-934
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-097-5/
%R 10.4153/CJM-1975-097-5
%F 10_4153_CJM_1975_097_5

[1] 1. Ganea, T., Lusternik-Schnirelmann category and cocategory, Proc. Lond. Math. Soc. 10 (1960), 623–639. Google Scholar

[2] 2. Ganea, T., Fibrations and cocategory, Comment. Math. Helv. 35 (1961). 15–24, Google Scholar

[3] 3. Ganea, T., Sur quelques invariants numériques du type d'homotopie. Cahiers de topologie et géométrie différentielle, Ehresmann Seminar, Paris, 1962. Google Scholar

[4] 4. Hilton, P. J., Homotopy theory and duality, Lecture Notes, Cornell University, 1959. Google Scholar

[5] 5. Maclane, S., Categories for the working mathematician, (Springer-Verlag, Berlin, 1971). Google Scholar

[6] 6. Quillen, D. G., Homotopical algebra, Springer Lecture Notes 43, 1967. Google Scholar

[7] 7. G. W., Whitehead, The homology suspension, Colloque de Topologie Algébrique, Louivan 1956, pp. 89–95. Google Scholar

[8] 8. Whitehead, J. H. C., Combinatorial homotopy, I, Bull. Amer. Math. Soc. 55 (1949), 213–245. Google Scholar

Cité par Sources :