Quantum polynomial functors

The (strict) polynomial functors form a category equivalent to the polynomial representations for general linear groups. This functor interpretation provides a useful way to understand GLn representation theory. I will present a quantization of the polynomial functors, joint with Valentin Buciumas. Two important insights from the classical polynomial functors are the stability property and the composition of functors. I will describe these ideas and explain what generalizes and what does not generalize.