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On coalgebras and type transformations

H. Peter Gumm (2007)

Discussiones Mathematicae - General Algebra and Applications

We show that for an arbitrary Set-endofunctor T the generalized membership function given by a sub-cartesian transformation μ from T to the filter functor 𝔽 can be alternatively defined by the collection of subcoalgebras of constant T-coalgebras. Sub-natural transformations ε between any two functors S and T are shown to be sub-cartesian if and only if they respect μ. The class of T-coalgebras whose structure map factors through ε is shown to be a covariety if ε is a natural and sub-cartesian mono-transformation....

On Cohen-Macaulay rings

Edgar E. Enochs, Jenda M. G. Overtoun (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we use a characterization of R -modules N such that f d R N = p d R N to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the d t h local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R .

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