nLab initial algebra

Idea

An initial algebra is an initial object in a category (or higher category) of algebras.

There are many meanings of ‘algebra’, so many meanings of ‘initial algebra’. Most cases are fairly vacuous, but we could probably list them here. Some cases, however, are rather important and interesting in the topic of induction and recursion:

• initial algebra of an endofunctor,

• initial algebra of a presentable (infinity,1)-monad.

Examples

List them here if you like:

• (…)

References

• Jiří Adámek, Stefan Milius, Lawrence Moss: Initial Algebras and Terminal Coalgebras: The Theory of Fixed Points of Functors, Cambridge University Press (2025) [doi:10.1017/9781108884112, draft:pdf-archived]