Inserter category
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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(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 [math]\displaystyle{ G(h) \circ f = g \circ F(h) }[/math].[1]
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.[2]
References
- ↑ Seely, R. A. G. (1992). Category Theory 1991: Proceedings of an International Summer Category Theory Meeting, Held June 23-30, 1991. American Mathematical Society. ISBN 0821860186. https://books.google.com/books?id=3hwiWc4iau0C. Retrieved 11 February 2017.
- ↑ Adámek, J.; Rosický, J. (10 March 1994). Locally Presentable and Accessible Categories. Cambridge University Press. ISBN 0521422612. https://books.google.com/books?id=iXh6rOd7of0C. Retrieved 11 February 2017.
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