POE Injector + 10 Gbps Switch

Hi,

I have an odd use case in which a team needs local 10 Gbps switching with POE. I see very few 10 Gbps switches that do it, but maybe I'm just not looking in the right places.

I have a simple question about POE injectors: can you plug one into a 10 Gbps (obviously copper) switch port and expect it to work as it would in the more typical use case with a slower copper port? I understand that doing this will necessarily slow down the port to whatever speed the injector is rated for.

Thanks!