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In the previous post, I explained how Weihrauch reducibility could be viewed as a dependent lens. That was supposed to be the start of a few blog posts because my supervisor thought this work probably wasn't publishable. However, since then, we have written this up, and a preprint is available on the Arxiv. Even better, this work was accepted for CiE, as was an abstract for TYPES. I might still write some blog posts on various container constructions, but today I want to talk about the strong (or uniform) variant of Weihrauch Reducibility.

A short while ago, we had CCA 2024 at Swansea, which I attended mostly because it was local and my supervisor was giving a talk. The first day had a session dedicated to the topic of Weihrauch reducibility, during which it occurred to me that the definition of Weihrauch reducibility looked suspiciously similar to the definition of a dependent lens and that some of the operators on Weihrauch degrees should just be known constructions on polynomials. She agreed, telling me that Weihrauch problems are the polynomials in the category \(\PasmFull\) of partitioned assemblies over the PCA \(\Ktwo\) filtered by \(\Ktworec\).

If I'm honest, I'm only writing this page so that my site doesn't seem completely empty, but that doesn't mean I don't have posts planned. Famous last words, I suppose. Over the next few weeks, I plan to upload some of the writing I've already done as part of my PhD research, including a more leisurely introduction to the ideas in a paper that my Supervisor and I have just submitted to a conference. Stay tuned for automata theory, type theory and category theory.