Examples of functor

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The functor syntax admits functors of many variables, and functor composition.
Similar to the noun chunk identification algorithm discussed above, the verb chunking based on supertags can be performed using local functor-argument information encoded in supertags.
It is easily seen that this is indeed a functor.
Since we are working with complexes of vector spaces, the functor () is exact.
This is not the standard representation of the exponent in a functor category.
However, it does not map identities to identities, so it does not extend to a functor between the full categories.
Consequently, the function space appearing in the functor induced by m is turned into a set of relations.
To get a core functor, we must extend the object map (-)0 to functions.
It is easy to see that this functor is full and faithful.
The next step in the categorical treatment is to try to make the notion of faithful copy a functor.
A functor is a graph morphism that preserves identities and composition.
It is easy to check that the functor preserves the identity map and composition.
The idea is to show that this functor is uniform on maps and to express other functors in terms of it.
Most of the definition is a routine generalisation of that of monoidal functor.
Categorically, it will be defined as the final coalgebra of the lift functor.
Functions can be encoded within the featurevalue map representation such that the functor annotates the feature-value map and the arguments are features.

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