# On coalgebras and type transformations

Discussiones Mathematicae - General Algebra and Applications (2007)

- Volume: 27, Issue: 2, page 187-197
- ISSN: 1509-9415

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topH. Peter Gumm. "On coalgebras and type transformations." Discussiones Mathematicae - General Algebra and Applications 27.2 (2007): 187-197. <http://eudml.org/doc/276913>.

@article{H2007,

abstract = {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.},

author = {H. Peter Gumm},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {coalgebra; endofunctor; filter functor; cartesian transformation; crisp},

language = {eng},

number = {2},

pages = {187-197},

title = {On coalgebras and type transformations},

url = {http://eudml.org/doc/276913},

volume = {27},

year = {2007},

}

TY - JOUR

AU - H. Peter Gumm

TI - On coalgebras and type transformations

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2007

VL - 27

IS - 2

SP - 187

EP - 197

AB - 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.

LA - eng

KW - coalgebra; endofunctor; filter functor; cartesian transformation; crisp

UR - http://eudml.org/doc/276913

ER -

## References

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- [5] H.P. Gumm, From{T-coalgebras to filter structures and transition systems, pp. 194-212 in: D.H. Fiadeiro et al., eds, Algebra and Coalgebra in Computer Science, vol 3629 of Lecture Notes in Computer Science, Springer 2005. Zbl1151.18001
- [6] H.P. Gumm and T. Schröder, Coalgebras of bounded type, Math. Struct. in Comp. Science 12 (2001), 565-578. Zbl1011.08009
- [7] H.P. Gumm and T. Schröder, Types and coalgebraic structure, Algebra Universalis 53 (2005), 229-252. Zbl1086.08002
- [8] E.G. Manes, Implementing collection classes with monads, Math. Struct. in Comp. Science 8 (1998), 231-276. Zbl0916.68016
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- [10] J.D.H. Smith, Permutation representations of left quasigroups, Algebra Universalis 55 (2006), 387-406. Zbl1117.20051

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