Kate thinks that Jack's hiding something in the Hatch.

She has asked questions about Locke and him spending so much time there, do you need somebody to give you a break typoing in the numbers? Uh, no.
Jack tell Sun to tell the truth with Jin. Jack believes you should deal with people honestly. Immediately Kate asks of things are okay in the hatch. Oh, yeah, just fine. Then, this week, she asks of she could use the shower, and you can tell from the way she looks at Jack while he's making up an andswer about the shower's hot water being broken, that she knows he's lying.

That's what's up with Kate cozying up to Jack.

She wants to know what's going on and why Jack's lying to everybody. That, and the fact that he keeps zinging her for all the times she hasn't told the truth is probably entering into the equation here, too.

Paybacks can get kind of nasty sometimes, and I think this one's gonna be a doozy.

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charlie98210
"Whoa!" she said. "Cry 'Havoc!' And let loose the dogs of war!"
And, like Banquo's ghost, they just won't go away.