Properties preserved under equivalence of categories I would like to ask about properties that are preserved under equivalence of categories. To be more specific, is it true that equivalences preserve limits? Why?

Basically any property that can be considered categorical in nature. Any textbook would list a warning if a property isn't preserved. Wikipedia lists some simple examples.
Here are some things that aren't necessarily preserved:

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*Number of objects

*Number of morphisms (total)

*Underlying graph

*Other evil properties

Tip for Proofs:
Equivalences preserve hom-sets. This helps, for example, if you are trying to proof that a morphism is unique.
