Adding attribute to category and display category as per that attribute

Question

Magento by default provide adding attribute to the products but not to the category.Is there any way to add attribute to the category? I would like to have attribute with input type- multiple select .

My question is explained in 2 parts.

Detail eg:

Part 1: I have a player(category) called XYZ and it should have attribute like team name. When i say multiple select it means,player can be part of different teams.So i will select lets say 3 team names.

so

• player XYZ belongs to team A,B,C
• player ABC belongs to team A,B
• player PQR belongs to team B,C

Part 2: Now i want to include this teams A,B,C in the menu(frontend) and

• when i select team A -> it will display all players who have team A (attribute) selected
• Same for B,C.

Thank you