Usually a hard sided cat carrier is used in the dog crate as well as a small litter box.
When I adopt an outdoor cat or one that has been TNR'd and is still in a trap I just set up the large crate with litter box and cat carrier and then release the trapped cat into the crate which has worked well for me. I did make a temporary door from flexible vinyl fencing with a hole cut in it slightly larger than the trap for one particular cat though.
I do use a small bungee cord with hooks to keep the cat carrier open so the cat can hide in it. When it's time to feed, clean litter, etc. make sure the cat is in the carrier, unlatch the bungee hook and use a long heavy stick (I use PVC pipe) and stick it through the bars of the cage to close the carrier door and then perpendicular to the carrier to keep the carrier door closed. Open the crate door, making sure the cat is still in the carrier and then latch the carrier door securely.
Check out the article Feral cat set up long term for a better explanation of what I wrote above.
When I adopt an outdoor cat or one that has been TNR'd and is still in a trap I just set up the large crate with litter box and cat carrier and then release the trapped cat into the crate which has worked well for me. I did make a temporary door from flexible vinyl fencing with a hole cut in it slightly larger than the trap for one particular cat though.
I do use a small bungee cord with hooks to keep the cat carrier open so the cat can hide in it. When it's time to feed, clean litter, etc. make sure the cat is in the carrier, unlatch the bungee hook and use a long heavy stick (I use PVC pipe) and stick it through the bars of the cage to close the carrier door and then perpendicular to the carrier to keep the carrier door closed. Open the crate door, making sure the cat is still in the carrier and then latch the carrier door securely.
Check out the article Feral cat set up long term for a better explanation of what I wrote above.