<div id="comment:0"></div> Currently, the category for `DefaultConvertMap`s is `SetsWithPartialMaps()`. ``` sage: type(QQ[['x']].coerce_map_from(QQ)) <type 'sage.structure.coerce_maps.DefaultConvertMap_unique'> sage: QQ[['x']].coerce_map_from(QQ).category_for() Category of sets with partial maps ``` In contrast, ``` sage: QQ.hom(QQ[['x']]).category_for() Category of euclidean domains ``` Depends on #23201 Component: **coercion** Keywords: **sd86.5** Author: **David Roe, Julian Rüth** Branch: **[`5eccb52`](https://github.com/sagemath/sagetrac-mirror/commit/5eccb5217999af4dc094b8a21d8b00071457c04d)** Reviewer: **Julian Rüth, David Roe** _Issue created by migration from https://trac.sagemath.org/ticket/23184_