Why do cats sleep all the time?

Actually, female cats do not sleep as much as males.  A well fed cat, who does not need to hunt will relax and that involves sleep.

To get them to play, find what toy they like most, use that to initiate play.  Or just be content to sit with them and stroke them, it is very soothing to sit with a sleeping cat and stoke them.  Very good for your heart.

Because,our cats have breed just that.Just look to the stray cats they do not sleep much because they have not any breed ! <3 xx

Most cats are female and that's what females do.

Also, cats will sleep when they feel safe.

Therefore, if your cat is nervous on its own it will  not sleep, but when you come home it feels safe enough to sleep, and is too tired to play.

Cats sleep an average of 15 hours a day, and some even sleep 20 hours in a 24h period. 

They sleep most of the day and become active only around twilight. Cats are predators, and hunt a night, that's why they sleep most of the day. And a indoor cat will sleep more than a cat who roams outside!