I don't know where to post this cat eats ants so how do you kill them?

I live in an apartment and I have these tiny, tiny ants. They are called sugar ants. I can't use ant traps because I have 1 cat that will eat them off the floor when she sees them.

I looked up natural remedies but as with a variety of spices and then chemicals like borax, I thought I would come here and see if anyone has had any similar experiences.

If you see where they're getting in, you can use caulk to block their entry points. Ants follow pheromone paths that are laid down by an ant that has found food, so even if the food is gone they still follow the path. So when you clean, try to wipe down wherever they've walked. You don't have to use a harsh chemical, just whatever you normally use to clean counter tops and such. I think vinegar is a good cat safe cleaner. Removing the "there is food here" message should reduce their numbers. 

If they're going for cat food, I've had some success with putting the bowl up on a little box. It confuses the ants enough that they can't find it easily.

The ants I've had problems with are much bigger, but the most success I've had has been with caulking up holes. I found where most of them were getting in on the outside wall. If you know what time of day they're most active, you can go looking and you should see a nice steady line of ants scurrying in and out.

We had an ant invasion a year ago when AT&T workers kicked up a nest. I got rid of them by placing bundles of sage and rosemary in the areas they were invading. Smells nice, looks pretty, and safely repels ants.

You can use ant baits IF you have a way to ensure cat can't eat them!
I was able to put one under a low cabinet out of reach, and I made another cat-proofed using soda bottles and duct tape... I put holes in the plastic the ants could fit through, cut the bottle and placed a bait inside, then thoroughly duct taped it closed. Then I taped the whole contraption to my kitchen counter in the middle of the ant highway. Worked really well. Careful about some ant baits that are liquid and can spill though.