Quillen cohomology and Baues-Wirsching cohomology of algebraic, theories

M. Jibladze; T. Pirashvili

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2006)

  • Volume: 47, Issue: 3, page 163-205
  • ISSN: 1245-530X

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Jibladze, M., and Pirashvili, T.. "Quillen cohomology and Baues-Wirsching cohomology of algebraic, theories." Cahiers de Topologie et Géométrie Différentielle Catégoriques 47.3 (2006): 163-205. <http://eudml.org/doc/91705>.

@article{Jibladze2006,
author = {Jibladze, M., Pirashvili, T.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {algebraic theories; Quillen cohomology; Baues-Wirshing cohomology; natural systems},
language = {eng},
number = {3},
pages = {163-205},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Quillen cohomology and Baues-Wirsching cohomology of algebraic, theories},
url = {http://eudml.org/doc/91705},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Jibladze, M.
AU - Pirashvili, T.
TI - Quillen cohomology and Baues-Wirsching cohomology of algebraic, theories
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2006
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 47
IS - 3
SP - 163
EP - 205
LA - eng
KW - algebraic theories; Quillen cohomology; Baues-Wirshing cohomology; natural systems
UR - http://eudml.org/doc/91705
ER -

References

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  2. [2] Michael Barr and Charles Wells, Toposes, triples and theories, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 278, Springer-Verlag, New York, 1985. Zbl0567.18001MR771116
  3. [3] Hans-Joachim Baues, Combinatorial foundation of homology and homotopy, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1999, Applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions. Zbl0920.55001MR1707308
  4. [4] Baues, Hans-Joachim; Jibladze, Mamuka; Tonks, Andy Cohomology of monoids in monoidal categories. (English) Loday, Jean-Louis (ed.) et al., Operads: Proceedings of renaissance conferences. Special session and international conference on moduli spaces, operads, and representation theory/operads and homotopy algebra, March 1995/May-June 1995, Hartford, CT, USA/Luminy, France. Providence, RI: American Mathematical Society. Contemp. Math.202, 137-165 (1997). Zbl0860.18006MR1436920
  5. [5] Hans-Joachim Baues and Andy Tonks, On sum-normalised cohomology of categories, twisted homotopy pairs and universal toda brackets, Quart. J. Math.47 (1996), no. 188, 405-433. Zbl0868.55009MR1460232
  6. [6] HansJoachim Baues and Günther Wirsching, Cohomology of small categories, J. Pure Appl. Algebra38 (1985), no. 2-3, 187-211. Zbl0587.18006MR814176
  7. [7] J.M. Boardman and R.M. Vogt, Homotopy invariant algebraic structures on topological spaces, Springer-Verlag, Berlin, 1973, Lecture Notes in Mathematics, Vol. 347. Zbl0285.55012MR420609
  8. [8] John W. Gray, Formal category theory: adjointness for 2-categories, Springer-Verlag, Berlin, 1974, Lecture Notes in Mathematics, Vol. 391. Zbl0285.18006MR371990
  9. [9] Luc Illusie, Complexe cotangent et déformations. II, Springer-Verlag, Berlin, 1972, Lecture Notes in Mathematics, Vol. 283. Zbl0238.13017MR491681
  10. [10] Mamuka Jibladze and Teimuraz Pirashvili, Cohomology of algebraic theories, 137 (1991), no. 2, 253-296. Zbl0724.18005MR1094244
  11. [11] Mamuka Jibladze and Teimuraz Pirashvili, Linear extensions and nilpotence of maltsev theories, Beitr. Algebra Geom.46, No. 1, 71-102 (2005). Zbl1081.18008MR2146444
  12. [12] Saunders MacLane, Categories for the working mathematician, Springer-Verlag, New York, 1971, Graduate Texts in Mathematics, Vol. 5. Zbl0232.18001MR354798
  13. [13] Barry Mitchell, Rings with several objects, Advances in Math.8 (1972), 1-161. Zbl0232.18009MR294454
  14. [14] Quillen, Daniel G. "Homotopical algebra." Lecture Notes in Mathematics, No. 43Springer-Verlag, Berlin-New York1967iv+156 pp. Zbl0168.20903MR223432
  15. [15] Quillen, Daniel G.On the (co-) homology of commutative rings. 1970 Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968) pp. 65-87. Amer. Math. Soc., Providence, R.I. Zbl0234.18010MR257068
  16. [16] W.H. Rowan, Enveloping ringoids, Algebra Universalis35 (1996), no. 2, 202-229. Zbl0853.08005MR1383659

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