We discuss the gluing construction of class S chiral algebras in derived setting. The gluing construction in non-derived setting was introduced by Arakawa to construct a family of vertex algebras of which the associated varieties give genus 0 Moore-Tachikawa symplectic varieties. Motivated by the higher genus case, we introduce a dg vertex algebra version of the category of Moore-Tachikawa symplectic varieties, where taking associated schemes gives a functor to the category of derived Moore-Tachikawa varieties. This talk is based on the preprint arXiv:2004.10055.

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