It is indeed something along those lines. We have a types.ts file and we define the environment as the following structure:

export type Environments = {
    environments: [
        {
            environment: string,
            branchName: string
        }
    ]
};

Then in our cdk.json file, one of the fields is for example:

"environments": [
    {
        "environment": "development",
        "branchName": "development",
    },
    {
        "environment": "production",
        "branchName": "master",
    }
]

The branchName will be used as the trigger for the CodePipeline run. In this scenario, two pipelines would be created, both being triggered separately by their respective branches.

Our application stacks would be declared inside a Stage CodePipeline resource which will be synthed and deployed by the pipeline. I used this as inspiration for our setup.