Sulfate hydrate refers to any sulfate salt that has been hydrated, or combined with water. In cosmetic formulation, it's more common to see specific sulfate hydrates like Sodium Laureth Sulfate (SLES) and Sodium Lauryl Sulfate (SLS).
SLES and SLS are both types of surfactants, which are compounds that lower the surface tension between two substances, such as oil and water. This is what allows soaps and shampoos to spread easily over your skin and hair, and helps to mix water with the oil and dirt on your skin, allowing it to be washed away.
However, sulfates are known to be quite harsh and can strip away too much oil from your skin and hair, leading to dryness and irritation. That's why you often see "sulfate-free" as a selling point on many cosmetic products. Still, they are effective cleaning agents and are used in a variety of cosmetic formulations for that purpose.
Just to clarify, the term "sulfate hydrate" is not commonly used in the cosmetic industry. It's much more common to refer to the specific type of sulfate being used, like SLES or SLS.
Also, it's important to note that "sulfate" in cosmetics does not refer to the same thing as "sulfites" or "sulfates" in food and wine, which some people are allergic to. The sulfates used in cosmetics are salts of sulfuric acid, not the same as the sulfites used as preservatives in food and wine.