Storing templated derived classes in container

I have a series of field validators that each look something like the following:

template <typename T>
class NameValidator : public Validator<T> {

    ...
    bool validate(const T& msg) const override { ... }
    ...

};

Each of these validators must be able to validate different message types, hence the template parameter T.

I would like to create a manager class that serves as a common gateway to each of these validators. Something like the following:

class ValidatorManger {

    ...
    // Calls validate() functions for each field.
    template <typename T>
    bool validate(const T& msg) { ... }
    ...

};

Hence, I will need to store each of the validator classes (ex: NameValidator<T>) in some type of data structure and then iterate over them within ValidatorManager::validate().

Is there a way to do this so that I do not have to explicitly specialize the templates for each message type? I'm imaging something like the following

validator_map.insert(std::pair("Name", NameValidator<T>));
validator_map.insert(std::pair("Age", AgeValidator<T>());
...

though this is obviously gibberish.

Questions:

• Has anyone used this sort of pattern before and have a solution for achieving this?
• Should I be rethinking this design entirely?