A Simple Characterization of Theories of Varieties

✍ Scribed by M.C. Pedicchio; R.J. Wood

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 153 KB
• Volume: 233
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8447

✦ Synopsis

We answer the question of which theories in the sense of Gabriel and Ulmer give rise to (finitary, multi-sorted) varieties and exhibit the 2-category of varieties as a (non-full) bireflective sub-2-category of the 2-category of locally finitely presentable categories. A central role is played by those objects, which we call effective projectives, whose hom functors preserve coequalizers of reflexive graphs.