nLab categorical algebra

Contents

category theory

Applications

Algebra

higher algebra

universal algebra

Contents

Idea

Broadly speaking, categorical algebra is algebra seen from and generalized via the point of view of category theory. Thus it studies those aspects of categorical and category-like constructions which are in the spirit of pure algebra.

First and foremost this includes the study of monoidal category theory, and the corresponding notions of monoid objects, module objects.

More generally, it is about the study of

1. algebras over$\,$ algebraic theories,

2. algebras over$\,$ monads,

3. algebras over$\,$ operads.

An account of the basics may be found at geometry of physics – categories and toposes in the section Basic notions of categorical algebra.

References

Exposition of basics of monoidal categories and categorical algebra: