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.
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Definition
If C and D are two categories and F and G are two functors from C to D, the inserter category Ins(F,G) is the category whose objects are pairs (X,f) where X is an object of C and f is a morphism in D from F(X) to G(X) and whose morphisms from (X,f) to (Y,g) 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(F,G) is also locally presentable.