nLab
Lex

$\mathrm{Lex}$ is a widely used name for the 2-category of:

• small finitely complete categories,

• finite-limit-preserving functors between these, and

• natural transformations between those.

In categorical logic, such categories are also known as finite limits theories or essentially algebraic theories. Finite-limit-preserving functors are also known as left exact functors or lex functors, and these give $\mathrm{Lex}$ its name.

category: category