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Proceedings of the American Mathematical Society

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On Spanier's higher order operations

Author: Yuh-ching Chen
Journal: Proc. Amer. Math. Soc. 31 (1972), 601-604
MSC: Primary 55.32; Secondary 18.00
MathSciNet review: 0288758
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Abstract: Given a stack $ A$ over a simplicial set $ K$, we construct the generalized Eilenberg-Mac Lane complexes $ K(A,n)$ that represents a stack cohomology theory over $ K$. We show that the higher order operations defined by Spanier are some sections of $ K(A,n)$ over $ K$ for some stack $ A$.

References [Enhancements On Off] (What's this?)

  • [1] Y. C. Chen, Stacks, costacks and axiomatic homology, Trans. Amer. Math. Soc. 145 (1969), 105-116. MR 40 #3536. MR 0250297 (40:3536)
  • [2] E. H. Spanier, Higher order operations, Trans. Amer. Math. Soc. 109 (1963), 509-539. MR 28 #1622. MR 0158399 (28:1622)

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Keywords: Higher order operations, generalized Eilenberg-Mac Lane complexes, injective cogenerators, cohomology representation theorem, obstructions to extending null-homotopies, cross sections
Article copyright: © Copyright 1972 American Mathematical Society

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