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According to the famous result of Schiffmann and Vasserot, the cohomology of the ADHM moduli space carries the structure of an affine-Yangian module. For the purpose of our talk, it is useful to view this moduli space from a three-dimensional perspective of the derived category of coherent sheaves on $\mathbb{C}^3$. More concretely, one can interpret the ADHM moduli space as parametrizing extensions of a coherent sheaf on $\mathbb{C^2}\subset \mathbb{C}^3$ by skyscraper sheaves. It is then natural to ask whether exchanging such a "framing" non-compact sheaf by a different one leads to other representations of the algebra. In this talk, I am going to give an overview of some of the developments in this direction and comment on various predictions originating from physics.