English

A two-dimensional Birkhoff's theorem

Category Theory 2015-09-03 v1

Abstract

Birkhoff's variety theorem from universal algebra characterises equational subcategories of varieties. We give an analogue of Birkhoff's theorem in the setting of enrichment in categories. For a suitable notion of an equational subcategory we characterise these subcategories by their closure properties in the ambient algebraic category.

Keywords

Cite

@article{arxiv.1509.00763,
  title  = {A two-dimensional Birkhoff's theorem},
  author = {Matěj Dostál},
  journal= {arXiv preprint arXiv:1509.00763},
  year   = {2015}
}
R2 v1 2026-06-22T10:47:38.289Z