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What is the difference of $\text{CAT}^{\mathbb T}$ from $\text{VAR}$ in this paper sketched below?

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    $\begingroup$ They are defined in the passage. Can you be more specific about your problem? $\endgroup$ – Kevin Carlson Jun 7 at 4:05
  • $\begingroup$ I just want to know what is the intuitive difference between $VAR$ and $CAT^T$ i.e. easily understandable by a beginner. $\endgroup$ – user122424 Jun 7 at 12:52
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Being the category of models of an algebraic theory is not itself characterized by algebraic axioms. The algebraic hull is the smallest 2-category with an algebraic description containing all categories of models of algebraic theories.

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  • $\begingroup$ OK. What is this thing: $\text{CAT}^{\mathbb T}$ ? What are 0-cells and 1-cells of it? Then 2-cells will be all n.t., right? $\endgroup$ – user122424 Jun 7 at 16:51
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    $\begingroup$ I would suggest following the citation in the paper to the definition of the Eilenberg-Moore 2-category of a 2-monad. That's what the citations are there for. $\endgroup$ – Kevin Carlson Jun 7 at 17:54

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