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categorical algebra

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.

Related concepts

• universal algebra

References

• Francis Borceux, Handbook of Categorical Algebra, III Vols.

See also

• Wikipedia, Categorical algebra