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: 2-dimensional universal algebra, equational subcategories
2010 MSC: 18C10, 18C15
Theory and Applications of Categories, Vol. 31, 2016, No. 4, pp 73-100.