Relative fixed points of functors

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Schoen, Ezra and Master, Jade and Kupke, Clemens (2025) Relative fixed points of functors. Fundamenta Informaticae, 194 (2). 1. ISSN 0169-2968 (https://doi.org/10.46298/fi.12374)

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Abstract

We show how the relatively initial or relatively terminal fixed points for a well-behaved functor form a pair of adjoint functors between -coalgebras and -algebras. We use the language of locally presentable categories to find sufficient conditions for existence of this adjunction. We show that relative fixed points may be characterized as (co)equalizers of the free (co)monad on . In particular, when is a polynomial functor on the relative fixed points are a quotient or subset of the free term algebra or the cofree term coalgebra. We give examples of the relative fixed points for polynomial functors and an example which is the Sierpinski carpet. Lastly, we prove a general preservation result for relative fixed points.

ORCID iDs

Schoen, Ezra, Master, Jade and Kupke, Clemens ORCID logoORCID: https://orcid.org/0000-0002-0502-391X;
CORE (COnnecting REpositories)