Enriched Lawvere Theories
Enriched Lawvere Theories
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丰富的劳维尔理论
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通讯作者：
J. Power
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作者：
J. Power
我们定义了富Lawvere理论的概念，即在一个monoidal双闭范畴V上的富化，该范畴V是局部唯一可表示为闭范畴的。证明了丰富Lawvere理论的范畴等价于V. Moonad上的nitary monad范畴，Lawvere V-理论的模型的V-范畴等价于相应的V-monad的代数的V-范畴.这一切都例行延伸到当地的体面相对于任何正规红衣主教。最后讨论了V是Cat的特殊情形，并解释了这种对应如何推广到代数的伪映射上。
We deene the notion of enriched Lawvere theory, for enrichment over a monoidal biclosed category V that is locally nitely presentable as a closed category. We prove that the category of enriched Lawvere theories is equivalent to the category of nitary monads on V. Morever, the V-category of models of a Lawvere V-theory is equivalent to the V-category of algebras for the corresponding V-monad. This all extends routinely to local presentability with respect to any regular cardinal. We nally consider the special case where V is Cat, and explain how the correspondence extends to pseudo maps of algebras.