Topos Institute Colloquium, 5th of September 2024.
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I will argue that applied category theory would benefit, both practically and strategically, from greater attention to user interface. Starting from some very basic examples, I will discuss some of the conceptual challenges in this area and explain how they map onto categorical structures like monads, comonads and polynomial functors. I will close with a discussion of the Semagrams user interface library, its goals and future prospects.