do they have a women's team as well?
Yes, Arsenal Ladies F.C.
Arsenal F.C.
Arsenal Women is the women's football club affiliated to Arsenal. Founded as Arsenal Ladies F.C. in 1987 by Vic Akers, they turned semi-professional in 2002 and are currently managed by Clair Wheatley. 
how many times have arsenal won the double Three what sports is this club associated with? English football when was this club established? October 1886
wiki:1536871
Arsenal F.C. [SEP] Arsenal Women
Arsenal Women is the women's football club affiliated to Arsenal. Founded as Arsenal Ladies F.C. in 1987 by Vic Akers, they turned semi-professional in 2002 and are currently managed by Clair Wheatley. Akers currently holds the role of Honorary President of Arsenal Women. As part of the festivities surrounding their 30th anniversary in 2017, the club announced that they were changing their formal name to Arsenal Women F.C., and would use "Arsenal" in all references except rare cases where there might be confusion with the men's side. Arsenal Women are the most successful team in English women's football having won a total of 58 trophies.