Conference Paper/Proceeding/Abstract 5 views
Problems with fixpoints of polynomials of polynomials
Cécilia Pradic 
,
Ian Price
,
Ian Price
Logic in Computer Science 2026
Swansea University Authors:
Cécilia Pradic , Ian Price
Abstract
Motivated by applications in computable analysis, we study fixpoints of certain endofunctors over categories of containers. More specifically, we focus on fibred endofunctors over the fibrewise opposite of the codomain fibration that can be themselves be represented by families of polynomial endofun...
| Published in: | Logic in Computer Science 2026 |
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| Published: |
Lipics
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| Online Access: |
https://arxiv.org/abs/2601.15420 |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa71916 |
| Abstract: |
Motivated by applications in computable analysis, we study fixpoints of certain endofunctors over categories of containers. More specifically, we focus on fibred endofunctors over the fibrewise opposite of the codomain fibration that can be themselves be represented by families of polynomial endofunctors. In this setting, we show how to compute initial algebras, terminal coalgebras and another kind of fixpoint ζ. We then explore a number of examples of derived operators inspired by Weihrauch complexity and the usual construction of the free polynomial monad.We introduce ζ-expressions as the syntax of \mu-bicomplete categories, extended with \zeta-binders and parallel products, which thus have a natural denotation in containers. By interpreting certain ζ-expressions in a category of type 2 computable maps, we are able to capture a number of meaningful Weihrauch degrees, ranging from closed choice on {0, 1} to determinacy of infinite parity games, via an "answerable part" operator. |
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| College: |
Faculty of Science and Engineering |