Mixed Hodge structures over $F\otimes \mathbb{R}$

Question

Let $F$ be a number field. Nekovàř, on page 18 of Values of L-functions and p-adic cohomology, is referring to the category of mixed Hodge structures over $F\otimes_{\mathbb{Q}} \mathbb{R}$. Can anyone precise the definition of the above?

Many thanks!