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On sifted homotopy colimits of algebras over an $N_{\infty}$-operad

Gregoire Marc

Abstract

We prove that the forgetful functor from algebras over an $N_{\infty}$-operad to equivariant spaces preserves sifted homotopy colimits

On sifted homotopy colimits of algebras over an $N_{\infty}$-operad

Abstract

We prove that the forgetful functor from algebras over an -operad to equivariant spaces preserves sifted homotopy colimits

Paper Structure

This paper contains 3 sections, 17 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Counter example
  3. Cellular extensions of strong fixed cofibrant operads

Key Result

Theorem A

Let ${\mathcal{O}}$ be a $G$-simplicial operad. We denote by ${\mathscr{S}}^G$ the $\infty$-category of equivariant spaces, by $\operatorname{sSet}^G$ the category of $G$-simplicial sets, and by $W_G$ the class of morphisms of ${\mathcal{O}}$-algebras which forget to $G$-weak equivalences. If for ev preserves sifted colimits. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (38)

  • Theorem A: \ref{['nsifco']}
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Definition 1
  • ...and 28 more