Category theory MOC

Monoidal internalization

Roughly speaking, (monoidal) internalization¹ is a process by which algebraic constructions are formulated in the language of the Cartesian category so that they can be imported into other monoidal categories, dualized, and generalized.

Internalized structures

• Magma object, Magma morphism
• Semigroup object, Semigroup morphism,

Monoids and friends

• Monoid object, Monoid morphism,
• Comonoid object, Comonoid morphism,
• Bimonoid object, Bimonoid morphism,
• Hopf monoid object, Hopf monoid morphism, Category of Hopf monoids

Modules and fiurends

• Module object

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