On a generalized small-object argument for the injective subcategory problem

J. Adámek; H. Herrlich; J. Rosický; W. Tholen

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2002)

  • Volume: 43, Issue: 2, page 83-106
  • ISSN: 1245-530X

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Adámek, J., et al. "On a generalized small-object argument for the injective subcategory problem." Cahiers de Topologie et Géométrie Différentielle Catégoriques 43.2 (2002): 83-106. <http://eudml.org/doc/91656>.

@article{Adámek2002,
author = {Adámek, J., Herrlich, H., Rosický, J., Tholen, W.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {reflective category; locally presentable category; topological category; injective object; factorization system; locally ranked category},
language = {eng},
number = {2},
pages = {83-106},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {On a generalized small-object argument for the injective subcategory problem},
url = {http://eudml.org/doc/91656},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Adámek, J.
AU - Herrlich, H.
AU - Rosický, J.
AU - Tholen, W.
TI - On a generalized small-object argument for the injective subcategory problem
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2002
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 43
IS - 2
SP - 83
EP - 106
LA - eng
KW - reflective category; locally presentable category; topological category; injective object; factorization system; locally ranked category
UR - http://eudml.org/doc/91656
ER -

References

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  1. [1] J. Adámek, H. Herrlich and G.E. Strecker: Abstract and Concrete Categories, John Wiley, New York1990. Zbl0695.18001MR1051419
  2. [2] J. Adámek, H. Herrlich, J. Rosický and W. Tholen: Injective hulls are not natural, to appear in Alg. Univ. Zbl1061.18010MR1967087
  3. [3] J. Adámek and J. Rosicky: Locally presentable and accessible categories, Cambridge University Press, 1994. Zbl0795.18007MR1294136
  4. [4] T. Beke: Sheafifiable homotopy model categories, Math. Proc. Cambridge Philos. Soc.129 (2000), 447-475. Zbl0964.55018MR1780498
  5. [5] C. Cassidy, M. Hebert, G.M. Kelly: Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc.38 (1985), 287-329. Zbl0573.18002MR779198
  6. [6] P. Gabriel and F. Ulmer: Lokal Präsentiebare Kategorien, Springer Lecture Notes Math. 221, Springer-VerlagBerlin, 1971. Zbl0225.18004MR327863
  7. [7] P. Gabriel and M. Zisman: Calculus of fractions and homotopy theory, Springer-VerlagBerlin, 1967. Zbl0186.56802MR210125
  8. [8] M.D. Hirschhorn: Localizations of model categories, preprint 1998, http://www.math.mit.edu/psh. 
  9. [9] H. Herrlich: Almost reflective subcategories of Top, Topology Appl.49 (1993), 251-264. Zbl0805.54016MR1208677
  10. [10] M. Kelly: A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on, Bull. Austral. Math. Soc.22 (1980), 1-84. Zbl0437.18004MR589937
  11. [11] V. Koubek and J. Reiterman: Categorical constructions of free algebras, colimits and completions of partial algebras, J. Pure Appl. Algebra14 (1979), 195-231. Zbl0403.18002MR524187
  12. [12] D. Quillen: Homotopical algebra, Lecture Notes Math. 43, Springer-Verlag, Berlin1967. Zbl0168.20903MR223432
  13. [13] J. Reiterman: Categorical algebraic constructions, Charles University dissertation (in Czech), Prague1976. 
  14. [14] C.M. Ringel: Diagonalisierungspaare I., Math. Z.117 (1970), 240-266. Zbl0206.30002MR272864

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