Yes Sam,without a doubt it is ,Kadota.
Grown in California for fig paste production.
It needs a lot of long hot season,so if you do not live in Central California ,the fruits that appear after July 15 will never ripe so remove them right away to have the tree direct resources to the fruits that will be able to ripe.

I brought it in because it's getting colder it lost 4 leaves.Do I keep it indoors all winter long or I just put it outside till it loose his leaves and then I bring it in my garage?I have tasted some of its figs and they were really good ,but can they ripe indoors?Are you sure this is this specie because I was thinking of a more commun one because I live in canada....

Thanks again

There is no more common fig than Kadota.
And ,yes I am sure,it is.
As for how to take care,you will have to read post about it here on fig Forum,and Figs4fun.
There is a lot of care to be successful next year and have fruits again.
Any mistake and by by, fruits.