The left derived tensor product of 𝒞𝒜𝒯 valued diagrams

Murray Heggie

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1992)

  • Volume: 33, Issue: 1, page 33-53
  • ISSN: 1245-530X

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Heggie, Murray. "The left derived tensor product of $\mathcal {CAT}$ valued diagrams." Cahiers de Topologie et Géométrie Différentielle Catégoriques 33.1 (1992): 33-53. <http://eudml.org/doc/91489>.

@article{Heggie1992,
author = {Heggie, Murray},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {category of small categories; Quillen's homotopical algebra; categories of diagrams; homotopy colimits; Grothendieck construction},
language = {eng},
number = {1},
pages = {33-53},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {The left derived tensor product of $\mathcal \{CAT\}$ valued diagrams},
url = {http://eudml.org/doc/91489},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Heggie, Murray
TI - The left derived tensor product of $\mathcal {CAT}$ valued diagrams
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1992
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 33
IS - 1
SP - 33
EP - 53
LA - eng
KW - category of small categories; Quillen's homotopical algebra; categories of diagrams; homotopy colimits; Grothendieck construction
UR - http://eudml.org/doc/91489
ER -

References

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  1. 1 J. Benabou, Les Distrib-uteurs, Rapport no. 33, janvier 1973, Seminair des Mathematiques Pure, Institut de Mathematique Pure et Appliquee, Universite Catholique de Louvain. 
  2. 2 P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Ergebnisse der Math ematik und ihrer Grenzgebiete, Band 35, Springer Verlag, Berlin and New York, 1967. Zbl0186.56802MR210125
  3. 3 J. Giraud, Methode de la Descente, Bull. Soc. Math. France, no. Memoire2 (1964). Zbl0211.32902MR190142
  4. 4 J. Gray, Fibred and Co-Fibred Categories, Conference on Categorical Algebra, Springer Verlag, Berlin and New York, 1965, pp. 21-83. Zbl0192.10701MR213413
  5. 5 ____, The Representation of Limits, Lax Limits and Homotopy Limits as Sections, Mathematical Applications of Category Theory, Amer. Math. Soc.Contemporary Math. Series 30, 1984. Zbl0541.18010MR749769
  6. 6 R. Guitart, Des Machines aux Bimodules, Thèse, Amiens, 1979. 
  7. 7 R. Guitart and L. van den Bril, Calcul des Satellites et Presentation des bimodules a l'Aide des Carres Exactes, Cahiers de Topologie et Geometrie DifferentielleXXIV-3 (1983), 299-330. Zbl0533.18007MR728635
  8. 8 M. Heggie, Tensor Products in Homotopy Theory, Ph.D. Thesis, McGill University, 1986. 
  9. 9 G.M. Kelly, Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Note Series64, Cambridge University Press, Cambridge, 1982. Zbl0478.18005MR651714
  10. 10 S. MacLane, Categories for the Working Mathematician, Graduate Texts in Mathematics, no. 5, Springer Verlag, Berlin and New York, 1971. Zbl0232.18001MR354798
  11. 11 R. Paré, Connected Components and Colimits, Journal of Pure and Applied Algebra3 (1973), 21-42. Zbl0255.18003MR338112
  12. 12 D. Quillen, Homotopical Algebra, Lecture Notes in Math.43, Springer Verlag, Berlin and New York, 1967. Zbl0168.20903MR223432
  13. 13 ____, Higher Algebraic K-Theory I, Lecture Notes in Mathematics341, Springer Verlag, Berlin and New York, 1973, pp. 85-147. 
  14. 14 R. Thomason, Homotopy Colimits in the Category of Small Categories, Math. Proc. Camb. Phil. Soc.85 (1979), 91-109. Zbl0392.18001MR510404

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