By which I mean a category of models for a Lawvere theory.
I have not seen this anywhere, so I wonder if something goes wrong with this category.
2026-03-25 03:02:47.1774407767
Is the category of groupoids a Lawvere thory?
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Assuming you don't mean magmas, the answer is "no". Categories and groupoids are not models of a Lawvere theory because composition isn't a total operation. However, they are essentially algebraic which is very similar to being a model of a Lawvere theory. Basically, instead of finite-product preserving functors, you consider finite limit preserving functors. This is needed because composition is only defined over a pullback. Roughly, an essentially algebraic theory is like an algebraic theory except that you are allowed to have "partial" operations.