from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. a structure that is dual to unital associative algebras
Finally, our work incorporates many ideas and results coming from the coalgebra research community in the years following the publication of Aczel 1988.
This was not so much because it raised questions about set theory, but rather because it showed the value of using the categorical notion of a coalgebra.
We shall also be concerned with situating both the mathematics and the underlying intuitions in a broader picture, one derived from work in coalgebra.
But it quickly became apparent that this notion of coalgebra could be studied on its own, that themes from the book had a field of application much wider than pure set theory.
Incorporating concepts and results from category theory, coalgebra leads us to concepts such as corecursion and coinduction; these are in a sense duals to the more standard notions of recursion and induction.
_*: Stream a - > StObserve a data StObserve (a: Set): Set where empty: StObserve a nonempty: a - > Stream a - > StObserve a appears in the domain, rather than the range of _* because we are defining a coalgebra and