The university and the company are jointly building a laboratory.
Tips
register
Heavily used in news and policy register, especially around 一带一路 (Yídài Yílù, Belt and Road) and 共建共享 (gòngjiàn gòngxiǎng, jointly build and share). Sounds bureaucratic in casual speech — use 一起建 (yìqǐ jiàn) for everyday 'build together'.