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Pointed integral coalgebras and R-local homotopy theory

Manfred Stelzer

Abstract

We show that, for a principal ideal domain R, the homotopy category of Bousfield R-local spaces injects fully faithful into a homotopy category of simplicial pointed flat coalgebras.

Pointed integral coalgebras and R-local homotopy theory

Abstract

We show that, for a principal ideal domain R, the homotopy category of Bousfield R-local spaces injects fully faithful into a homotopy category of simplicial pointed flat coalgebras.

Paper Structure

This paper contains 12 sections, 57 theorems, 161 equations.

Table of Contents

  1. Introduction
  2. Recollections on Purity and Purification
  3. Pure irreducibility
  4. Group like elements in flat coalgebras
  5. Pure irreducible components
  6. Splitting off the pure coradical
  7. Pure filtrations of coalgebras
  8. The pure coradical filtration
  9. Categorical properties of pointed coalgebras
  10. Simplicial flat pointed coalgebras
  11. Proof of the main theorem
  12. Pointed coalgebras, binomial algebras and Galois action

Key Result

Theorem 1.1

$\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (118)

  • Theorem 1.1
  • Theorem 1.2
  • Definition 2.1
  • Definition 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Lemma 2.7
  • Lemma 2.8
  • ...and 108 more