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Godement resolution and operad sheaf homotopy theory

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Abstract

We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric \(\Omega \)-spectra, filtered dg algebras, operads and operad algebras.

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Notes

  1. So, in particular, example (2.1.6) proves that the Thom–Whitney simple functor of [5, 25] is a realization of a homotopy limit too.

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Acknowledgments

This paper develops an idea suggested to us by Vicente Navarro. We owe him a debt of gratitude for sharing it with us. The second-named author also benefited from many fruitful conversations with Pere Pascual. We are indebted to Francisco Guillén, Fernando Muro, Luis Narváez and Abdó Roig for their comments. We also thank the anonymous referee for suggesting a reorganization of the paper which, we believe, improves its clarity.

Author information

Authors and Affiliations

  1. ICMAT, CSIC-Complutense-UAM-CarlosIII, Campus Cantoblanco, UAM, 28049, Madrid, Spain

    Beatriz Rodríguez González

  2. Dept. Matemàtica Aplicada (MAT), Universitat Politècnica de Catalunya, UPC, and BGSMath, Diagonal 647, 08028, Barcelona, Spain

    Agustí Roig

Authors
  1. Beatriz Rodríguez González
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  2. Agustí Roig
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Correspondence to Agustí Roig.

Additional information

B. R. González partially supported by ERC Starting Grant project TGASS and by contracts SGR-119 and FQM-218. A. Roig partially supported by projects MTM2012-38122-C03-01/FEDER and 2014 SGR 634.

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Rodríguez González, B., Roig, A. Godement resolution and operad sheaf homotopy theory. Collect. Math. 68, 301–321 (2017). https://doi.org/10.1007/s13348-016-0171-5

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