  Leveraging skew Howe duality, we show that Lawson-Lipshitz-Sarkar's
spectrification of Khovanov's arc algebra gives rise to 2-representations of
categorified quantum groups over $\mathbb{F}_2$ that we call spectral
2-representations. These spectral 2-representations take values in the homotopy
category of spectral bimodules over spectral categories. We view this as a step
toward a higher representation theoretic interpretation of spectral
enhancements in link homology. A technical innovation in our work is a
streamlined approach to spectrifying arc algebras, using a set of canonical
cobordisms that we call frames, that may be of independent interest. As a step
towards extending these spectral 2-representations to integer coefficients, we
also work in the $\mathfrak{gl}_2$ setting and lift the Blanchet-Khovanov
algebra to a multifunctor into a multicategory version of
Sarkar-Scaduto-Stoffregen's signed Burnside category.
