What do you think about placing text labels (description) from a tab menu into an app bar?
Does this comply with Google material design? And is it helpful from UX point of view?
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I think the common way is this:
Parent (title) - child (tab) - child(tab) - child(tab)
What tab(child) is selected should be shown with different transparency of the selected tab text/icon, not the title.
Your case is a bit misleading because it breaks this parent/child relation.
Common solution would be to put your main sections into navigation drawer (sidebar) or in a bottom bar, and use tabs for filtering each section (for example - missed calls, outgoing calls, incoming calls etc.)
This is not exactly a frequently used of title bar but yes, such a solution does comply with Material Design. Take for example the YouTube app in which the title changes according to which tab you are in.
The general idea is that the title can change if what would be written there otherwise (in this case: Youtube) wouldn't be of importance to the user as they actually know what app they are in.
This kind of solution is only used in one-page apps. In the case of apps like the Play Store where there are many pages and categories, the title doesn't change according to the tab as the user actually needs to know what page they are in whether it is history, all apps, updates etc. Using a solution where the title changes would be very confusing to the user as the same text (like Games) could appear in multiple places (for example in Trending and on the home page). Thus, the title in the top bar represents the page which is open, not the selected tab.
In YouTube this is not a problem as there is only one page and Subscribtions appear only on the home page. A solution with the changing title only saves space and does not affect the functionality or ease of use.