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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1126,
author = {H. Peter Gumm},
title = {On coalgebras and type transformations},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {187-197},
zbl = {1146.68400},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1126}
}
H. Peter Gumm. On coalgebras and type transformations. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 187-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1126/
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