Help with Gige poE camera pinout

Hello,

To keep it short, I want to build a cable that plugs into the camera, then into a poE injector, then into a PC.

Pic 3 shows the poE injector (pins4&5 ++) (pins 7&8 --).

Pic2 is the camera data sheet. It notes the protocol.

Pic 1 shows the camera pinout for the rj45.

Do I need to crossover somewhere so the injector pins4&5, 7&8 go to the correct spot?

Thanks for your time.

build computervision data hello notes poe protocol shows