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CALCO
2011
Springer

Bases as Coalgebras

7 years 6 months ago
Bases as Coalgebras
Abstract. The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be understood as bases, decomposing each element x into primitives elements from which x can be reconstructed via the operations of the algebra. This holds in particular for the free vector space monad, but also for other monads. For instance, continuous dcpos or stably continuous frames, where each element is the join of the elements way below it, can be described as such coalgebras. Further, it is shown how these coalgebras-on-algebras give rise to a comonoid structure for copy and delete, and thus to diagonalisation of endomaps like in linear algebra.
Bart Jacobs
Added 13 Dec 2011
Updated 13 Dec 2011
Type Journal
Year 2011
Where CALCO
Authors Bart Jacobs
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