A two-dimensional Birkhoff's theorem

Matej Dostal

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.

Published 2016-01-12.


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