Named for a fabric made in Baghdad, it's a cat with a striped or brindled coat
In Arabic the cloth was known as 'attb, from Al-'Attbya, the name of its... [DOC] [TLE] Definition of tabby - Merriam-Webster's Student Dictionary [PAR] Etymology: from French tabis "a silk fabric with a lustrous wavy finish," from Latin 
... ya, name of a part of Baghdad where the cloth was made 1 : a domestic cat 
with a striped and spotted coat ...