Ventilation in Closet

Im planning to grow in my closet and my idea was to build a cabinet and have it in the closet with the doors closed. Im living in a apartment so I wouldnt be able to cut any holes in the walls or ceiling. Theres a 1'' gap under the closet door to my room, my idea was to exhaust the air above the cabinet into the closet with the doors closed and have aluminum ducting from the cabinet and have it going under the closet doors and hooked up to a pc fan. Would this work or would i need to exhaust the hot air somewhere else. My room is always cool because i have a portable ac and a ceiling fan but i was just wondering if this would work, my only other option is to exhaust it in my room, my neighbors live above me so the attic is not an option, any advice?

i would just cut a hole in the door at the top to vent out into your room. i think the duct crunched to an inch being pulled by a a weak pc fan wont be enough. i would not build a cab in your closet but use the whole closet if possible. do you have an openable window close to the closet? or a bathroom with a fart fanclose by?

Odor control is key in apartment locations. Id recommend going the scrubber (carbon filter) + centrifugal fan + exhaust duct combo. Vent and odor control A+. Just have the carbon filter inside the cabinet, run the duct exhaust from cabinet into your room with the AC. Odor gone, heat mixed with AC, and the cabinet/grow tent has fresh air coming in.

Yea if its going to be in a closet, im thinking of the 2ft deep 5-6 ft long closet with sliding doors. Might as well use the entire closet, well to give you a watered down answer im sure you can bring some plants to harvest in their. But you must know from the get go, you will encounter issues and may be frustrating in the beginning. & Know your elec bill will rise. Due to the constant AC and such.

cacamel: my closet is on the opposite side of the window so i cant run the ducting from there, and the bathroom isnt anywhere near my room but i do have a spare bathroom fan if that can be used for anything. I was thinking of just buying another closet door so i can make 2 holes for the intake/exhaust and just replace the door when im done but id also like to make it as stealth as possible.
The dimensions of my closet are 4' x 2' x 6' +

If i bought an exhaust/carbon filter inline fan and built the grow box, could i just exhaust the air into the closet and have the closet doors open a bit so cool air gets in? What kind of intake fan would i need? sorry for all the questions, ive been researching for months because I just want it done the right way and ventilation was something i never fully understood. I also plan to have 1 or 2 fans in the grow box to circulate the air, would this work to keep the heat down?