Coherent categories with respect to monads and coherent prohomotopy theory

M. A. Batanin

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1993)

  • Volume: 34, Issue: 4, page 279-304
  • ISSN: 1245-530X

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Batanin, M. A.. "Coherent categories with respect to monads and coherent prohomotopy theory." Cahiers de Topologie et Géométrie Différentielle Catégoriques 34.4 (1993): 279-304. <http://eudml.org/doc/91530>.

@article{Batanin1993,
author = {Batanin, M. A.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {Kleisli categories; homotopy classes; coherent homotopy categories; unlocalised homotopy category; coherent prohomotopy},
language = {eng},
number = {4},
pages = {279-304},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Coherent categories with respect to monads and coherent prohomotopy theory},
url = {http://eudml.org/doc/91530},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Batanin, M. A.
TI - Coherent categories with respect to monads and coherent prohomotopy theory
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1993
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 34
IS - 4
SP - 279
EP - 304
LA - eng
KW - Kleisli categories; homotopy classes; coherent homotopy categories; unlocalised homotopy category; coherent prohomotopy
UR - http://eudml.org/doc/91530
ER -

References

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  1. 1 Batanin M.A., About the coherent prohomotopy category of Lisica-Mardesič and generalized Steenrod homology theories (Russian), Preprint 1986. 
  2. 2 Bauer F.W., A shape theory with singular homology, Pacific J. Math.64 (1976), 25-76. Zbl0346.55014MR436130
  3. 3 Bauer F.W., Under what condition are shape homology E* and Steenrod homology sE* isomorphic?Lecture Notes in Math.870, Springer (1981), 186-214. Zbl0503.55002MR643531
  4. 4 Boardmann J.M. & Vogt R.M., Homotopy invariant algebraic structures in topological spaces, Lecture Notes in Math.347, Springer (1973). Zbl0285.55012MR420609
  5. 5 Bousfield A.K. & Kan D.M., Homotopy limits, completions and localizations, Lecture Notes in Math.304, Springer (1972). Zbl0259.55004MR365573
  6. 6 Bolisfield A.K. & Kan D.M., The homotopy spectral sequence of a space with coefficients in a ring, Topology11 (1972), 79-106. Zbl0202.22803MR283801
  7. 7 Cathey F.W. & Segal J., Strong shape theory and resolutions, Topology and its Appl.15 (1983), 119-130. Zbl0505.55012MR686090
  8. 8 Cordier J.-M., Extensions de Kan simplicialement cohérentes, Prépublications Amiens1985. 
  9. 9 Cordier J.-M., Homologie de Steenrod-Sitnikov et limites homotopiques algébriques, Manuscripta Math. 59 (1987), 35-52. Zbl0643.55003MR901248
  10. 10 Cordier J.-M., Comparaison de deux catégories d'homotopie de morphismes cohérents, Cahiers Top. & Geom. Diff. Cat.XXX (1989), 257-275. Zbl0679.55006MR1029628
  11. 11 Cordier J.-M. & Porter T., Vogt's Theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Phil. Soc.100 (1986), 65-90. Zbl0603.55017MR838654
  12. 12 Edwards P.A. & Hastings H.M., Cech and Steenrod homotopy theories with applications to Geometric Topology, Lecture Notes in Math.542, Springer (1976). Zbl0334.55001MR428322
  13. 13 Gabriel P.& Zisman M., Calculus of fractions and homotopy theory, Springer1967. Zbl0186.56802MR210125
  14. 14 Kelly G.M., Basic concepts of enriched category theory, Lecture Notes in Math.764, Springer (1982). Zbl0478.18005MR651714
  15. 15 Lisica J.T. & Mardesi S., Coherent prohomotopy and strong shape theory, Glasnic Matematiči s.111, v. 19 (1984), 335-400. Zbl0553.55009MR790021
  16. 16 Lisica J.T. & Mardesi S., Strong homology of inverse systems I, Top. & its Appl.19 (1985), 29-43. Zbl0559.55008MR786079
  17. 17 Lisica J.T. & Mardesic S., Strong homology of inverse systems II, Top. & its Appl.19 (1985), 45-64. Zbl0559.55008MR786080
  18. 18 Lisica J.T. & Mardesic S., Strong homology of inverse systems III, Top. & its Appl.20 (1985), 29-37. Zbl0574.55005MR798442
  19. 19 Lysica J.T., On strong theory of coshapes (Russian), Sibirski Mat. Z.24 (1983), 81-99. 
  20. 20 Maclane S., Categories for the working mathematician, Springer1971. Zbl0705.18001MR354798
  21. 21 Mardesi S. & Segal J., Shape Theory, North-Holland, 1982. Zbl0495.55001MR676973
  22. 22 May J.P., The geometry of iterated loop spaces, Lecture Notes in Math.271, Springer (1972). Zbl0244.55009MR420610
  23. 23 Meyer J.P., Bar and cobar constructions I, J. Pure & Appl. Algebra33 (1984), 163-207. Zbl0542.57036MR754954
  24. 24 Porter T., Coherent prohomotopy theory, Cahiers Top. & Geom. Diff. Cat.XIX (1978), 3-46. Zbl0387.55013MR496541
  25. 25 Porter T., On the two definitions of Ho(pro-C), Top. & its Appl.28 (1988), 289-293. Zbl0647.18008MR931529
  26. 26 Thomason R.W., Algebraic K-theory and etale cohomology, Ann. Scient. Ecole Normale Sup. XVIII-3 (1985), 437-552. Zbl0596.14012MR826102
  27. 27 Vogt P. M., Homotopy limits and colimits, Math. Z.134 (1973), 11-53. Zbl0276.55006MR331376

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