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[[Hall's marriage theorem]] gives necessary and sufficient conditions for a finite collection of not necessarily distinct, but non-empty sets to have a transversal.
In [[computer science]], computing transversals is useful in several application domains, with the input [[family of sets]] often being described as a [[hypergraph]].
==Systems of distinct representatives==
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==Category theory==
In the language of [[category theory]], a '''transversal''' of a collection of mutually disjoint sets is a [[Section (category theory)|section]] of the [[quotient map]] induced by the collection.
==Computational complexity==
The [[computational complexity]] of computing all transversals of an input [[family of sets]] has been studied, in particular in the framework of [[enumeration algorithm]]s.
==See also==
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