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Higher Lawvere theories
Journal of Pure and Applied Algebra ( IF 0.770 ) Pub Date : 2020-03-12 , DOI: 10.1016/j.jpaa.2020.106362
John D. Berman

We survey Lawvere theories at the level of ∞-categories, as an alternative framework for higher algebra (rather than ∞-operads). From a pedagogical perspective, they make many key definitions and constructions less technical. They also play a prominent role in equivariant homotopy theory and its relatives. Our main result establishes a universal property for the ∞-category of Lawvere theories, which completely characterizes the relationship between a Lawvere theory and its ∞-category of models. Many familiar properties of Lawvere theories follow directly. As a consequence, we establish a correspondence between enriched and module Lawvere theories, which implies that the Burnside category is a classifying object for additive categories. This completes a proof from our earlier paper on the commutative algebra of categories.
更新日期:2020-03-12

 

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