According to Archimate's specification for application, there are two different meta objects:

• Application Component
• Application Function

Check out ArchiMate® 3.0.1 Specification, 9 Application Layer.

The problem could be divided in two parts:

1. It becomes an arbitrary choice regarding how many levels could be used for respective meta objects. We advocate a prescriptive standard which has a logic and normative structure.
2. A closer consideration of the definitions shows us that there is a weak logic. The application component should be modular, but application module does not exist as an object. The application function is definied by clustering objects. But application task does not exist as an object.

A reasonable conclusion is that Archimate is structured in different levels, but it is not successful when it comes to the standards.

Another conclusion is that in order to standardize the architecture and facilitate the analysis and connections to other dimensions, a framework should contain 5 levels for application.

See Prime Arch's application Hierarchy.