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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeDec 1st 2020

Added a reference to Adámek-Rosický-Vitale.

• CommentRowNumber2.
• CommentAuthorDmitri Pavlov
• CommentTimeDec 1st 2020
• (edited Dec 1st 2020)

The book by Adámek–Rosický–Vitale uses a different definition of an algebraic category: an algebraic category is a category equivalent to the category of algebras over an algebraic theory, i.e., the category of functors T→Set that preserve finite products, where T is a small category with finite products.

This definition seems to be much more widely used these days than the older definition of Adámek–Herrlich–Strecker.

Should we adjust the article accordingly? Is the older definition of Adámek–Herrlich–Strecker actually used anywhere other than in their book?

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeDec 13th 2020

Added the original paper by Lawvere.

• CommentRowNumber4.
• CommentAuthorGuest
• CommentTimeJan 25th 2022
When is an abelian category algebraic?
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