# On the homotopy category of Moore spaces and the cohomology of the category of abelian groups

Hans-Joachim Baues; Manfred Hartl

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 3, page 265-289
- ISSN: 0016-2736

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topBaues, Hans-Joachim, and Hartl, Manfred. "On the homotopy category of Moore spaces and the cohomology of the category of abelian groups." Fundamenta Mathematicae 150.3 (1996): 265-289. <http://eudml.org/doc/212177>.

@article{Baues1996,

abstract = {The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.},

author = {Baues, Hans-Joachim, Hartl, Manfred},

journal = {Fundamenta Mathematicae},

keywords = {homotopy category; Moore spaces; cohomology; category of abelian groups; James-Hopf invariants},

language = {eng},

number = {3},

pages = {265-289},

title = {On the homotopy category of Moore spaces and the cohomology of the category of abelian groups},

url = {http://eudml.org/doc/212177},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Baues, Hans-Joachim

AU - Hartl, Manfred

TI - On the homotopy category of Moore spaces and the cohomology of the category of abelian groups

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 3

SP - 265

EP - 289

AB - The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.

LA - eng

KW - homotopy category; Moore spaces; cohomology; category of abelian groups; James-Hopf invariants

UR - http://eudml.org/doc/212177

ER -

## References

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- [8] H.-J. Baues and W. Dreckmann, The cohomology of homotopy categories and the general linear group, K-Theory 3 (1989), 307-338. Zbl0701.18009
- [9] H.-J. Baues and G. Wirsching, The cohomology of small categories, J. Pure Appl. Algebra 38 (1985), 187-211. Zbl0587.18006
- [10] K. A. Hardie, On the category of homotopy pairs, Topology Appl. 14 (1982), 59-69. Zbl0499.55002
- [11] P. Hilton, Homotopy Theory and Duality, Gordon and Breach, 1965.
- [12] I. M. James, Reduced product spaces, Ann. of Math. 62 (1955), 170-197.
- [13] M. Jibladze and T. Pirashvili, Cohomology of algebraic theories, J. Algebra 137 (1991), 253-296. Zbl0724.18005
- [14] T. Pirashvili and F. Waldhausen, MacLane homology and topological Hochschild homology, J. Pure Appl. Algebra 82 (1992), 81-98. Zbl0767.55010
- [15] J. H. C. Whitehead, A certain exact sequence, Ann. of Math. 52 (1950), 51-110. Zbl0037.26101

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