Affine web of type Q

We introduce a new diagrammatic $\mathbb{k}$-linear monoidal supercategory $QWe{b}^{\bullet }$, the affine web supercategory of type $Q$, where $\mathbb{k}$ is a commutative ring of characteristic not two. This category is the affinization of the web category of type $Q$, originally introduced by Brown and Kujawa. It serves as the type $Q$ analog of the affine web category introduced by Davidson, Kujawa, Muth and Zhu, and independently by Wang and one of the authors. We obtain diagrammatic integral bases for the Hom-spaces of this category. We show that $QWe{b}^{\bullet }$ provides a combinatorial model for a natural monoidal supercategory of endosuperfunctors for Lie superalgebras of type $Q$. .