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According to the Wiktionary, kato originates from French, Italian, Latin, etc... and kata comes from kato + a. But how can we say that it is not the opposite? Can we say that the root kat- comes from French, Italian, Latin, etc... and depending on the suffix used, it defines the grammatical class of the word (like noun, adjective, ...)?

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In Esperanto, the root words themselves already have a meaning. So the root kat is already the animal and it is intrinsically a noun. Similarly, the root bel intrinsically represents the state of something so it is most naturally used as an adjective.

However, neither of these roots can be used alone without an ending to classify it, so even though kat is a noun, you need to add the -o to use it in a sentence. And bel needs to have -a if it is used as an adjective. These endings don’t change the base meaning.

On the other hand, adding -a to kat changes the meaning to be “like a cat”. So in that sense, kata is a derived word from the Esperanto word kato. Adding -a to bel doesn’t create a new meaning, so we wouldn’t say that bela is derived from belo.

So, I guess you could say that kato is just a declination of the root kat and that kata is a derived word with a different meaning. Wiktionary doesn’t have entries for the root words alone, so it has to have the root meaning under the article with the word with an ending. In this case the most logical ending to represent the root meaning of the root kat is kato.

As always, PMEG has a more detailed description of this.

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Linguistics categorizes words into noun, verb and other roots, so kat is more noun (kato), and lern is more verbal (lerni).

The number of occurrences of a suffix -o/-i/-a and other statistics play a role.

For Esperanto dictionaries that categorisation could play a role for the entry word:

  • kaso, kasisto
  • kato, kateca
  • kavo
  • ...
  • lerni, lernejo, lernanto

It also has some effects on the word forming:

  • esti alta = alti (rare)
  • esti kato = kati (to be avoided)

The arbitrary roots of different categories:

  • martelo / marteli (=hammer)
  • segi / segilo (=saw)
  • pinĉi / pinĉilo
  • though: ŝraŭbo / ŝraŭbi / ŝraŭbilo (=screw / screw driver)

But in general for Esperanto it is an unneeded categorisation.

More sense make verbal (in)transitivity.

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