Can a betta be kept with a Cory catfish?

No! Betta males are peacefull fish and mix well with most other species. They will only fight with other Betta males.

never mix a male betta with any other type of fish if you want to keep them alive..male bettas a solitary fish and most likely will kill anything in there with it..i know believe me...i heard that you can mix male bettas with ghost shrimp,neon tetras,and Cory cats..my betta has killed all of the above..i put some neon tetras and Cory cats with him and within 5 seconds the betta was killing a Cory cat

the above is incorrect. but the first one is right. What you have to do is when you get your betta, but him in a ziplock, half air half water; and but the ziplock in the aquarium. I left mine in their for a week ( yes, i fed him ) until he calmed down and realized the other fish weren't a threat or other bettas. Then open the bag and let him swim out. Yes, he may nip when a Cory cat comes near him or chase a fancy guppie or tetra, but he will calm down after about a day. If he dosent return him or put him back in the ziplock.

Also don't put the fish in the betta's cage, but the betta in the fish'es cage using the ziplock method. The betta will be more aggressive if fish invade his territory, but if he is in new territory he will be less aggressive.