Coalgebras Over a Commutative Ring
نویسنده
چکیده
By a coalgebra over the commutative ring K or a K-coalgebra, we understand a cocommutative, coassociative K-coalgebra with counit. More explicitly we mean a K-module C equipped with maps &C+C&C, subject to the requirement (where we write @ for OK) that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors; CAC@C 1 CC38 C@C e@'CtC@C@C, where we have, as usual, eliminated from this diagram an isomorphism between C @ (C 0 C) and (C @ C) @ C; C C@K +==CxC=K@C, 0 where the diagonal arrows are the canonical isomorphisms.
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تاریخ انتشار 2003