PreprintCC BY 4.0arXiv
Noetherian forms of free non-symmetric operads
Abstract
In this paper, we study certain categories of labeled finite rooted ordered trees over a fixed set of labels where each label is equipped with an arity: a fixed number of children that the vertex with the given label must have. Equivalently, these are expression trees for operations in a free non-symmetric operad. A morphism between these trees matches a pruning of one tree (a prefix) with an entire subtree of another (a suffix). We characterize such categories, up to isomorphism, in terms of suitable exactness properties. It turns out that these categories exhibit strong algebraic behavior, in the sense that every such category, when appended with a strict initial object, has a particularly nice noetherian form.
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BibTeX
@misc{janelidze2026noetherian,
title = {{Noetherian forms of free non-symmetric operads}},
author = {Zurab Janelidze},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10501},
eprint = {2609.10501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Noetherian forms of free non-symmetric operads
AU - Zurab Janelidze
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10501
UR - https://arxiv.org/abs/2609.10501
AB - In this paper, we study certain categories of labeled finite rooted ordered trees over a fixed set of labels where each label is equipped with an arity: a fixed number of children that the vertex with the given label must have. Equivalently, these are expression trees for operations in a free non-symmetric operad. A morphism between these trees matches a pruning of one tree (a prefix) with an entire subtree of another (a suffix). We characterize such categories, up to isomorphism, in terms of suitable exactness properties. It turns out that these categories exhibit strong algebraic behavior, in the sense that every such category, when appended with a strict initial object, has a particularly nice noetherian form.
ER -