# (Higher) extensions of mixed Hodge structures

Mixed Hodge structure is introduced by Deligne and it's very useful for studying complex algebraic varieties. We know $$\text{MHS}$$, the category of mixed Hodge structures is an abelian category. Where can I find a good reference for the computation of the (higher) extension groups inside MHS (and it's variations)? Carlson's paper "Extensions of mixed Hodge structures" is helpful, but I hope a more general reference.

For instance, let $$\text{MHS}^+_{\mathbb R}$$ denote the category of mixed Hodge structures equipped with an involution $$\phi_{\infty}$$ preserving the weight filtration and such that $$\phi_{\infty} \otimes c$$ preserves the Hodge filtration (here $$c$$ means complex conjugation). Is there no $$\operatorname{Ext}^{2}$$ in this category?

Beilinson, Notes on absolute Hodge cohomology is another reference. To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $$1$$, i.e. there is no $$Ext^i$$ for $$i>1$$. See 1.10 of Beilinson's paper.