Mapping spaces and R-completion

David Blanc, Debasis Sen

Research output: Contribution to journalArticlepeer-review


We study the questions of how to recognize when a simplicial set X is of the form X= map (Y, A) , for a given space A, and how to recover Y from X, if so. A full answer is provided when A= K(R, n) , for R= Fp or Q, in terms of a mapping algebra structure on X (defined in terms of product-preserving simplicial functors out of a certain simplicially enriched sketch Θ). In addition, when A= Ω A for a suitable connective ring spectrum A, we can recoverY from map (Y, A) , given such a mapping algebra structure. This can be made more explicit when A= K(R, n) for some commutative ring R. Finally, our methods provide a new way of looking at the classical Bousfield–Kan R-completion.

Original languageEnglish
Pages (from-to)635-671
Number of pages37
JournalJournal of Homotopy and Related Structures
Issue number3
StatePublished - 1 Sep 2018

Bibliographical note

Publisher Copyright:
© 2018, Tbilisi Centre for Mathematical Sciences.


  • Cosimplicial resolution
  • Mapping algebra
  • Mapping space
  • Rationalization
  • p-Completion

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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