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An evaluational category where morphisms satisfy the axiom of extensionality.
An extensional category is a evaluational category such that for morphisms and , if for all elements , then .
The category of sets and functions is an extensional category.
The category of monoids and monoid homomorphisms is an extensional category.
The category of $\mathbb{Z}$-modules and -module homomorphisms is an extensional category.
The category of $\mathbb{Z}$-algebras and -algebra homomorphisms is an extensional category.
The category of commutative rings and commutative ring homomorphisms is an extensional category.
The category of fields and field homomorphisms is an extensional category.
The category of Heyting algebras and Heyting algebra homomorphisms is an extensional category.
The category of frames and frame homomorphisms is an extensional category.
The category of set-truncated convergence spaces and continuous functions is an extensional category.
The category of set-truncated topological spaces and continuous functions is an extensional category.
The category of empty sets and functions is an extensional category.