User menu

A comonadic interpretation of Baues-Ellis homology of crossed modules

  • Open access
  • PDF
  • 272.24 K
  1. Barr Michael, Beck Jon, Homology and standard constructions, Seminar on Triples and Categorical Homology Theory (1969) ISBN:9783540046011 p.245-335, 10.1007/bfb0083087
  2. Baues Hans-Joachim, Combinatorial Homotopy and 4-Dimensional Complexes : , ISBN:9783110854480, 10.1515/9783110854480
  3. Beck, J.M.: Triples, Algebras and Cohomology, Reprints in Theory and Applications of Categories 2 (2003), 1–59, Ph.D. Thesis, Columbia University (1967)
  4. Borceux, F., Janelidze, G., Kelly, G.M.: Internal object actions. Comment. Math. Univ. Carolinae 46(2), 235–255 (2005)
  5. Bourn, D., Janelidze, G.: Protomodularity, descent, and semidirect products. Theory Appl. Categ. 4(2), 37–46 (1998)
  6. Breen Lawrence, Théorie de Schreier supérieure, 10.24033/asens.1656
  7. Brown Ronald, Ellis Graham J., Hopf Formulae for the Higher Homology of a Group, 10.1112/blms/20.2.124
  8. Brown, R., Huebschmann, J.: Identities Among Relations. Low-Dimensional Topology (Cambridge), London Mathematical Society Lecture Note series, vol. 46, pp. 153–202. Cambridge University Press, Cambridge (1982)
  9. Brown Ronald, Loday Jean-Louis, Van Kampen theorems for diagrams of spaces, 10.1016/0040-9383(87)90004-8
  10. Carrasco P., Cegarra A.M., Grandjeán A.R.-, (Co)Homology of crossed modules, 10.1016/s0022-4049(01)00094-9
  11. Casas J. M., Inassaridze N., Khmaladze E., Ladra M., Adjunction between crossed modules of groups and algebras, 10.1007/s40062-013-0073-0
  12. Cigoli, A.S., Gray, J.R.A., Van der Linden, T.: Algebraically coherent categories. Theory Appl. Categ. 30(54), 1864–1905 (2015)
  13. Datuashvili T, Pirashvili T, On (Co)Homology of 2-Types and Crossed Modules, 10.1006/jabr.2001.8919
  14. Donadze, G., Inassaridze, N., Porter, T.: $$n$$n-Fold Čech derived functors and generalised Hopf type formulas. K-Theory 35(3–4), 341–373 (2005)
  15. Ellis Graham J., Homology of 2-Types, 10.1112/jlms/s2-46.1.1
  16. Everaert, T.: An Approach to Non-abelian Homology Based on Categorical Galois Theory, Ph.D. thesis, Vrije Universiteit Brussel (2007)
  17. Everaert Tomas, Goedecke Julia, Van der Linden Tim, Resolutions, higher extensions and the relative Malʼtsev axiom, 10.1016/j.jalgebra.2012.07.036
  18. Everaert Tomas, Gran Marino, Protoadditive functors, derived torsion theories and homology, 10.1016/j.jpaa.2014.12.015
  19. Everaert Tomas, Gran Marino, Van der Linden Tim, Higher Hopf formulae for homology via Galois Theory, 10.1016/j.aim.2007.11.001
  20. Everaert, T., Van der Linden, T.: Baer invariants in semi-abelian categories II: Homology. Theory Appl. Categ. 12(4), 195–224 (2004)
  21. Forrester-Barker, M.: Representations of Crossed Modules and $${\rm Cat}^1$$Cat1-Groups. Ph.D. Thesis, University of Bangor (2003)
  22. Garzón, A.R., Miranda, J.G.: Homotopy theory for (braided) Cat-groups. Cah. Topol. Géom. Differ. Catég. XXXVIII(2), 99–139 (1997)
  23. GOEDECKE JULIA, VAN DER LINDEN TIM, On satellites in semi-abelian categories: Homology without projectives, 10.1017/s0305004109990107
  24. Grandjean A.R., Ladra M., Pirashvili T., CCG-Homology of Crossed Modules via Classifying Spaces, 10.1006/jabr.2000.8296
  25. Higgins P. J., Groups with Multiple Operators, 10.1112/plms/s3-6.3.366
  26. Inassaridze Hvedri, Non-Abelian Homological Algebra and Its Applications, ISBN:9789048148998, 10.1007/978-94-015-8853-9
  27. Janelidze George, Márki László, Tholen Walter, Semi-abelian categories, 10.1016/s0022-4049(01)00103-7
  28. Lavendhomme R., Roisin J.R., Cohomologie non abe´lienne de structures alge´briques, 10.1016/0021-8693(80)90168-4
  29. Mac Lane, S., Homology, G.M.: Wiss, vol. 114. Springer, Berlin (1967)
  30. Mac Lane, S.: Categories for the Working Mathematician, Graduate Texts in Mathematics, vol. 2, vol. 5. Springer, Berlin (1998)
  31. MacLane S., Whitehead J. H. C., On the 3-Type of a Complex, 10.1073/pnas.36.1.41
  32. Martins-Ferreira Nelson, Van der Linden Tim, A Note on the “Smith is Huq” Condition, 10.1007/s10485-010-9231-2
  33. Norrie, K.: Crossed Modules and Analogues of Group Theorems. Ph.D. Thesis, King’s College, University of London (1987)
  34. Norrie Katherine, Actions and automorphisms of crossed modules, 10.24033/bsmf.2140
  35. Weibel Charles A., An Introduction to Homological Algebra, ISBN:9781139644136, 10.1017/cbo9781139644136
  36. Whitehead J. H. C., Combinatorial homotopy. II, 10.1090/s0002-9904-1949-09213-3
Bibliographic reference Donadze, Guram ; Van der Linden, Tim. A comonadic interpretation of Baues-Ellis homology of crossed modules. In: Journal of Homotopy and Related Structures, Vol. 14, p. 625–646 (2019)
Permanent URL http://hdl.handle.net/2078.1/209743