nLab Lex

Idea

$Lex$ 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 $Lex$ its name.

Related concepts

$(n+1,r+1)$-categories of (n,r)-categories

• Pos

• Set

  • Rel

• Grpd, ∞Grpd

• Cat

  • Ho(Cat)

  • AccCat

  • PrCat

  • LexCat

  • MonCat

  • VCat

  • CatAdj

  • Prof

  • Operad

• 2Cat

• ModCat, CombModCat

• (∞,1)Cat

  • Pr(∞,1)Cat

  • (∞,1)Operad

• (∞,n)Cat

References

A study of descent in $Lex$:

• Marek Zawadowski?, Lax descent theorems for left exact categories (1995) (pdf)

category: category