Geodesic
A two-dimensional Birkhoff's theorem
Theory and applications of categories, Tome 31 (2016), pp. 73-100
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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.

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Classification : 18C10, 18C15
Keywords: 2-dimensional universal algebra, equational subcategories 
@article{TAC_2016_31_a3,
     author = {Matej Dostal},
     title = {A two-dimensional {Birkhoff's} theorem},
     journal = {Theory and applications of categories},
     pages = {73--100},
     year = {2016},
     volume = {31},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a3/}
}
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Matej Dostal. A two-dimensional Birkhoff's theorem. Theory and applications of categories, Tome 31 (2016), pp. 73-100. http://geodesic.mathdoc.fr/item/TAC_2016_31_a3/