Elliptic cohomology is unique up to homotopy

TL;DR

This paper proves that the sheaf defining the topological modular forms cohomology theory is unique up to homotopy, confirming the consistency of all prior constructions of Tmf.

Contribution

It provides a proof of the uniqueness of the sheaf defining Tmf, reconciling previous constructions without claiming originality.

Findings

Confirmed the uniqueness of the sheaf for Tmf up to homotopy

Reconciled all previous constructions of Tmf

Strengthened the theoretical foundation of topological modular forms

Abstract

Homotopy theory folklore tells us that the sheaf defining the cohomology theory Tmf of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of Tmf.