This portable cat prison (Amazon) fully incarcerates your feline friend and you can throw it on just like any other backpack.
From the product description:
Take your pet out to the ballgame, on a plane, or to the vet in your choice of colors and budget friendly designs. Small pets, such as cats and rabbits can be difficult to keep in carriers. Semi-sphere Design: semi-sphere can stop them from escaping and keeps them safe in your care.
Great tips in the Q&A section:
Question: What do i do if my animal needs to use the restroom
Answer: Take the cat out
I did not photoshop a screaming kitten into the product image. That is the one they market it with.