YOU SAID:

the cat cannot find its hat despite the fact that the cats hat is on the mat

INTO JAPANESE

猫の帽子がマットの上にあるにもかかわらず、猫はその帽子を見つけることができない

BACK INTO ENGLISH

the cat can't find its hat even though it's on the mat

INTO JAPANESE

猫はマットの上にいるにもかかわらず帽子を見つけられない

BACK INTO ENGLISH

The cat can't find his hat even though he's on the mat.

INTO JAPANESE

猫はマットの上にいても帽子を見つけられない。

BACK INTO ENGLISH

A cat can't find a hat even if it's on a mat.

INTO JAPANESE

猫はマットの上にいても帽子を見つけることができない。

BACK INTO ENGLISH

The cat can't find its hat even if it's on the mat.

INTO JAPANESE

猫はマットの上にいても帽子を見つけられない。

BACK INTO ENGLISH

A cat can't find a hat even if it's on a mat.

INTO JAPANESE

猫はマットの上にいても帽子を見つけることができない。

BACK INTO ENGLISH

The cat can't find its hat even if it's on the mat.