Inserter category

In category theory, a branch of mathematics, the inserter category is a variation of the comma category where the two functors are required to have the same domain category.

Definition

If C and D are two categories and F and G are two functors from C to D, the inserter category Ins is the category whose objects are pairs where X is an object of C and f is a morphism in D from F to G and whose morphisms from to are morphisms h in C from X to Y such that.

Properties

If C and D are locally presentable, F and G are functors from C to D, and either F is cocontinuous or G is continuous; then the inserter category Ins is also locally presentable.