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Synthetic spectra are (usually) cellular

Tyler Lawson

Abstract

If $E$ is a connective ring spectrum, then Pstragowski's category $Syn_E$ of $E$-synthetic spectra is generated by the bigraded spheres $S^{i,j}$. In particular, it is equivalent to the category of modules over a filtered ring spectrum.

Synthetic spectra are (usually) cellular

Abstract

If is a connective ring spectrum, then Pstragowski's category of -synthetic spectra is generated by the bigraded spheres . In particular, it is equivalent to the category of modules over a filtered ring spectrum.
Paper Structure (6 sections, 13 theorems, 27 equations)

This paper contains 6 sections, 13 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Graded projective modules
  3. Moore spectra
  4. Filtrations
  5. Cellularity of Moore spectra
  6. Cellularity of synthetic spectra

Key Result

Theorem 1.1

If $E$ is connective then the category $\mathop{\mathrm{Syn}}\nolimits_E$ of $E$-synthetic spectra from pstragowski-synthetic is cellular: it is generated under homotopy colimits by the bigraded spheres $S^{i,j}$.

Theorems & Definitions (25)

  • Theorem 1.1
  • Proposition 2.1
  • Corollary 2.2
  • Proposition 2.3
  • proof
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • Proposition 4.1
  • ...and 15 more