# Coassembly is a homotopy limit map

## TL;DR

This paper proves that the coassembly map functions as a homotopy limit map and demonstrates its equivalence to the homotopy limit map in equivariant A-theory, linking to the topological Riemann-Roch theorem.

## Contribution

It establishes the coassembly map as a homotopy limit map and connects it with bivariant A-theory in the context of the topological Riemann-Roch theorem.

## Key findings

- Coassembly map is a homotopy limit map.
- Homotopy limit map in equivariant A-theory matches coassembly map.
- Results relate to the topological Riemann-Roch theorem.

## Abstract

We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant $A$-theory agrees with the coassembly map for bivariant $A$-theory that appears in the statement of the topological Riemann-Roch theorem.