coalgebra love

# coalgebra

## Definitions

• n. a structure that is dual to unital associative algebras

## Etymologies

co- +‎ algebra (Wiktionary)

## Examples

• Finally, our work incorporates many ideas and results coming from the coalgebra research community in the years following the publication of Aczel 1988.

Non-wellfounded Set Theory

• 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.

Non-wellfounded Set Theory

• We shall also be concerned with situating both the mathematics and the underlying intuitions in a broader picture, one derived from work in coalgebra.

Non-wellfounded Set Theory

• 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.

Non-wellfounded 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.

Non-wellfounded Set Theory

• _*: 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