How to update a value of a nested object in a reducer?

This is very common thing, and, actually, quite daunting. As far as I know, there is no really good and well-adopted solution in plain JS. Initially, Object.assign approach was used:

return Object.assign({}, state, {
  categories: Object.assign({}, state.categories, {
    Professional: Object.assign({}, state.Professional, {
      active: true
    })
  })
});

This is too straightforward and cumbersome, I admit it, but I have to say that we've built few big applications with this approaches, and except for number of characters it is not bad. Nowadays, the most popular approach is using Object spread:

return {
  ...state,
  categories: {
    ...state.categories,
    Professional: {
      ...state.categories.Professional,
      active: true
    }
  }
}

The second approach is much more cleaner, so if you use plain JS, then it seems as a good choice. In Immutable.js I have to admit it is easier, you just do the next

return state.updateIn(['categories', 'Professional'], x => x.set('active', true));

But it has it's own drawbacks and caveats, so it is better to think about it seriously before committing to it.

And your last question regarding improving the state – usually it is better not to have such deep nesting (separate your concerns, very often fields don't depend on each other – like active status can be separated to another object), but it is hard to say because of no knowledge of your domain. Also, it is considered as normal thing to normalize your data.

The Redux docs section on Structuring Reducers covers this. In particular, see the section on Immutable Update Patterns. The examples given are for plain JS objects and arrays, but the same approach applies - map() over the list, return the existing item for everything you don't want to update and return a new version for the one you do want to update.

Per the docs, also note that it's easier to update a specific item if your data is stored in a normalized structure, since you can look it up by ID directly. The "Structuring Reducers" section covers normalization as well.