The Barista-Cats is the cafe that Quagmire opens in "Cat Fight".
But when Brian takes offense at it being next door to his favorite bar, he vows to shut it down. Making an argument that it's a health hazard, Brian actually succeeds in getting it shut down until the city council can rule on it. However, this backfires when Brian is no longer allowed in his bar either. This eventually causes a fight between Brian and Quagmire, but when Brian is struck by a passing bus, Quagmire stops to patch him up. As they chat, Quagmire admits he wanted to be known for something good instead of just being the town sex maniac. The city council eventually rules that animals can go in public places.