Kata is builded for 3v3 and 5v5 too. She can take quadra-kills, penta-kills. It isnt problem for this build.
Someone in your team must buy soul shroud! Beacause u got Lich Bane, no Nashor and you need CD reduce.
You must "steal" kills for stacks to Mejai's book. Your team must accept it! WHY LICH BANE?
Because this item get Kat rly big dmg. U use shunpo, which deal 600dmg and u'll kick him with normal attack,
but this attack do normal dmg + YOUR ABILITY POWER! This help you destroy tower in three kicks!


What to buy and how to play?!

1. boots+3hp pots
2. Mejai's + Sorcerer or Mercury boots
3. Rylai's Crystal Scepter
4. Lich bane
5. Zhonya's Ring
6. Void staff


At first time buy boots and 3x potion of health. Then you must buy Mejai's book and hunt enemies. After AP book of kills buy Sorcerer's boots. (If you play vs stunners and more, buy Mercury Treads) After boots u must buy Rylai's Crystal Scepter (or Zhonya vs Karthus) this will helps u slow enemies and kill them. Then u can buy Lich bane this item is rly great for Kata, because you'll do rly big dmg when you'll use ability.