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A concrete category with a good notion of evaluation of morphisms and elements.
An evaluational category is a concrete category with a function for objects and such that for morphisms and and elements , .
The category of sets and functions is an evaluational category.
The category of monoids and monoid homomorphisms is an evaluational category.
The category of $\mathbb{Z}$-modules and -module homomorphisms is an evaluational category.
The category of $\mathbb{Z}$-algebras and -algebra homomorphisms is an evaluational category.
The category of commutative rings and commutative ring homomorphisms is an evaluational category.
The category of fields and field homomorphisms is an evaluational category.
The category of Heyting algebras and Heyting algebra homomorphisms is an evaluational category.
The category of frames and frame homomorphisms is an evaluational category.
The category of set-truncated convergence spaces and continuous functions is an evaluational category.
The category of set-truncated topological spaces and continuous functions is an evaluational category.
The category of empty sets and functions is an evaluatioinal category.