And if we go to right hand side, you can see the cloud infrastructure, which includes managed services that managed application services on the cloud.

If we go the last of the right hand side, you can reach the fully Serverless services that we don’t any responsibility about servers, patches, updates and also not consider about scaling, reliability and availability so on.

And if we look the vertical way, you can see the separation of services:

Compute

Databases

Storage

Messaging / Application Integrations

Analytics

and we can put here API Management for AWS API Gateway.

https://medium.com/aws-lambda-serverless-developer-guide-with-hands/serverless-explained-with-aws-operational-responsibility-model-261030404fef