PreprintCC BY 4.0arXiv
On implicit operations and balanced categories
Abstract
The problem of determining whether a category is balanced (i.e., every morphism that is both an epimorphism and a monomorphism is an isomorphism) has been widely investigated, especially in algebra. For complete categories with an extremal projective generator, we characterise the property of being balanced, and the stronger property that every monomorphism is regular, in terms of implicit operations. These characterisations apply, for example, to any quasiequational class of algebras, possibly with a proper class of function symbols and unbounded arities, that admits free algebras.
Related
- Ideal balanced pairs in n-exangulated categories
- Well-balanced semi-implicit relaxed finite volume schemes for hyperbolic balance laws
- Strong isometric path complexity of graphs: Asymptotic minors, restricted holes, and graph operations
- WAMS Operations in modern power systems: A median expectation-based state estimation approach for grid resilience towards cyber attacks
- Homotopy operations on higher Lie algebras
BibTeX
@misc{reggio2026implicit,
title = {{On implicit operations and balanced categories}},
author = {Luca Reggio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15626},
eprint = {2609.15626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15626},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On implicit operations and balanced categories
AU - Luca Reggio
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15626
UR - https://arxiv.org/abs/2609.15626
AB - The problem of determining whether a category is balanced (i.e., every morphism that is both an epimorphism and a monomorphism is an isomorphism) has been widely investigated, especially in algebra. For complete categories with an extremal projective generator, we characterise the property of being balanced, and the stronger property that every monomorphism is regular, in terms of implicit operations. These characterisations apply, for example, to any quasiequational class of algebras, possibly with a proper class of function symbols and unbounded arities, that admits free algebras.
ER -