There isn't a universally agreed-upon system of categorizing enzymes into only three main categories. However, enzymes are most commonly classified based on the type of reaction they catalyze, which leads to six main classes:

1. Oxidoreductases: Catalyze oxidation-reduction reactions (transfer of electrons).

2. Transferases: Catalyze the transfer of functional groups (e.g., methyl, phosphate, amino groups).

3. Hydrolases: Catalyze the hydrolysis of bonds (using water).

4. Lyases: Catalyze the breaking of bonds without hydrolysis or oxidation, often forming a new double bond or ring.

5. Isomerases: Catalyze the rearrangement of atoms within a molecule, forming isomers.

6. Ligases: Catalyze the joining of two molecules, often using energy from ATP hydrolysis.

You could argue that these six classes can be broadly grouped into three categories:

* Hydrolases: Breaking down molecules (including oxidoreductases, which can be considered a special case of hydrolysis)

* Transferases: Transferring functional groups

* Ligases and Lyases: Creating and modifying molecules (excluding isomerases, which could be considered a sub-category of this group)

However, this categorization is simplified and may not accurately reflect the complexity of enzyme function. It's important to note that the six-class system is the most commonly used and accepted classification method.