nLab MonCat

Idea

$MonCat_{s}$ or $MonCat_\ell$ is the 2-category whose objects are monoidal categories, 1-morphisms are strong monoidal functors or lax monoidal functors, respectively, and whose 2-morphisms are monoidal natural transformations.

Related concepts

• monoidal adjunction

• change of enriching category

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