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In mathematics, coalgebras or cogebras are structures that are dual to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all arrows around, one obtains the axioms of coalgebras.
Every coalgebra, by duality, gives rise to an algebra, but not in general the other way. In finite dimensions, this duality goes in both directions.
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