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complete category
A category $\mathcal{C}$ is said to be a complete category if every small diagram has a limit, that is, a limiting cone exists over every small diagram (diagram such that collections of objects and morphisms are sets).
Of course, in a complete category, a product exists for any given set of objects. Also, a set of morphisms with common domain and codomain has an equalizer. Conversely, we have
in a category $\mathcal{C}$, if the product exists for an arbitrary set of objects, and the equalizer exists for any pair of morphisms with common domain and codomain, then $\mathcal{C}$ is complete.
Examples

Set is complete.

Group is complete.

Vector Space is complete

Rmodule is complete for a given unital ring $R$.

Topological Space is complete.
A category $\mathcal{C}$ is said to be finitely complete if every finite diagram (sets of objects and morphisms are finite) has a limit.
A similar sufficient condition for a category $\mathcal{C}$ to be finitely complete is for $\mathcal{C}$ to possess a terminal object and that a pullback exists for every pair of morphisms with common codomain.
Examples

Any complete category is clearly finitely complete.

The subcategories of the above examples consisting of all objects with finite cardinality are finitely complete (but not complete).
Remark. The dual notion of a complete category is that of a cocomplete category, and the dual of a finitely complete category is called a finitely cocomplete category.
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