Definition
Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:
- F : J → C.
The category J is thought of as index category, and the diagram F is thought of as indexing a collection of objects and morphisms in C patterned on J. The actual objects and morphisms in J are largely irrelevant—only the way in which they are interrelated matters.
One is most often interested in the case where the category J is a small or even finite category. A diagram is said to be small or finite whenever J is.
Read more about this topic: Limit (category Theory)
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