Wednesday, April 25, 2012

Category of equivalence relations

The functions square and abs are equivalence relation isomorphic to one another because they both partitioned the set of all real numbers into positive and negative segments. If there is a one to one correspondence between all equivalence classes induced by an equivalence relation then that equivalence relation also induces a partition of members.

The category of equivalence relations is partially ordered by a coarseness relation that determines rather or not an equivalence relation is coarser, finer, or equal to another equivalence relation.

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