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The phrase "are categorised by" is correct and usable in written English.
It can be used when describing how different items or concepts are classified or grouped based on certain criteria.
Example: "The species in this ecosystem are categorised by their feeding habits, such as herbivores, carnivores, and omnivores."
Alternatives: "are classified by" or "are grouped by".
Dictionary
are categorised by
verb
Standard spelling of from=non-Oxford British spelling
synonyms
Exact(30)
The rest are categorised by region.
All are categorised by age group.
The delays are categorised by the MS Society as unacceptable.
Incidents are categorised by detention centre staff according to guidelines from Transfield Services.
The different board games are categorised by length of play, and how much you want to rely on luck or skill.
The rooms are categorised by visual theme (exoticism, nature, Victorian gothic) and tell two stories side by side: that of McQueen's career, and of what it was like to go to a McQueen catwalk show.
Similar(30)
If I was a man I would resent being categorised by this 'wicked willy' view.
The EU's hotspot (pdf) approach, implemented in Italy and Greece late last year, allows migrants to be categorised by their nationality.
It's categorised by subjects like body parts - with covers that feature bellybuttons, that kind of thing.
They're right though, she is no Jackie or Marilyn because she refuses to be categorised by their male world.
For a century hotels have been categorised by their guests' budget, or proxies for it, such as the star scale.
More suggestions(20)
are construed by
are assigned by
are recognised by
are ventilated by
are viewed by
are characterised by
are catalogued by
are disaggregated by
are organized by
are collated by
are classified by
are apportioned by
are considered by
are conceptualized by
are designated by
are disbursed by
are described by
are characterized by
are differentiated by
are classifiable by
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com