In category theory if C is a category and a set-valued functor the category of elements of F (also denoted by ∫CF) is the category defined as follows:
- Objects are pairs where and .
- An arrow is an arrow in C such that .
A more concise way to state this is that the category of elements of F is the comma category where is a one-point set. The category of elements of F comes with a natural projection that sends an object (A,a) to A and an arrow to its underlying arrow in C.
Read more about Category Of Elements: The Category of Elements of A Presheaf
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