[[Category theory MOC]]
# Internalization

Roughly speaking, **internalization** is a process by which algebraic constructions are formulated in the language of the [[Cartesian category]] [[Category of sets]] so that they can be imported into other [[monoidal category|monoidal categories]], dualized, and generalized.

## Internalized structures

- [[Magma object]], [[Homomorphism of magma objects]]
- [[Semigroup object]], [[Homomorphism of semigroup objects]], [[Category of semigroup objects]]
- [[Monoid object]], [[Homomorphism of monoid objects]], [[Category of monoid objects]]
    - [[Comonoid object]], [[Homomorphism of comonoid objects]], [[Category of comonoid objects]]
- [[Module object]]

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