Is gender something more than our biology? Are our souls also gendered?

I tend to think our souls are also gendered given how differently men and women are. We think differently, we value different things, etc. Since these are functions of the mind, and the mind is a function of the soul, it seems to follow that there are different kinds of souls: male and female. Of course, it’s possible that these differences could be caused by hormonal differences between men and women. What do you think, and what are your reasons?