Mi vidas dormantan katon antaŭ la pordo, kaj apud la ŝaltita lampo kuŝas la malpura ombrelo.

Because katon is the direct object of vidas (I see), so it takes the accusative ending -n.

In Esperanto, adjectives must agree with the nouns they describe in:

• number
• case

So:

• kato = a cat
• katon = a cat, as a direct object
• dormanta kato = a sleeping cat
• dormantan katon = a sleeping cat, as a direct object

That is why both words end in -n here.

Dormantan comes from the verb dormi (to sleep) and the active present participle ending -ant-.

So:

• dormi = to sleep
• dormanta = sleeping / one who is sleeping
• dormantan = sleeping, in the accusative form

So dormantan katon means a sleeping cat or more literally a cat that is sleeping.

La is the definite article, meaning the.

So:

• pordo = door
• la pordo = the door
• antaŭ la pordo = in front of the door

Esperanto uses la much like English uses the. In this sentence, it refers to a specific door, not just any door.

They are two different prepositions:

• antaŭ = before, in front of
• apud = beside, next to, by

So:

• antaŭ la pordo = in front of the door
• apud la ŝaltita lampo = beside the switched-on/lit lamp

They describe different kinds of position.

Ŝaltita is a past passive participle from ŝalti, which means to switch on or to turn on.

So:

• ŝalti = to switch on
• ŝaltita = switched on / turned on

Therefore:

• la ŝaltita lampo = the switched-on lamp, or more naturally in English, the lit lamp / the lamp that is on

Both are adjectives, but they are attached to different nouns in different grammatical roles.

• ŝaltita lampo: this phrase is not a direct object, so there is no accusative -n
• dormantan katon: this phrase is the direct object of vidas, so both adjective and noun take -n

Compare:

• la ŝaltita lampo = the switched-on lamp
• mi vidas la ŝaltitan lampon = I see the switched-on lamp

In the second example, both words would take -n.

Esperanto word order is flexible. The normal English-like order would be:

La malpura ombrelo kuŝas apud la ŝaltita lampo.

But Esperanto can also say:

Apud la ŝaltita lampo kuŝas la malpura ombrelo.

This puts more focus on the location first: Beside the lit lamp lies the dirty umbrella.

Because Esperanto marks grammar clearly with endings, the word order can be changed more freely for style or emphasis.

Because ombrelo has no accusative -n, and the verb kuŝi is intransitive.

Kuŝi means to lie or to be lying and does not take a direct object. So the thing doing the lying must be the subject.

Thus:

• kuŝas la malpura ombrelo = the dirty umbrella is lying

Even though it comes after the verb, it is still the subject.

Pura means clean.

Esperanto often uses the prefix mal- to form the opposite:

• pura = clean
• malpura = dirty

This is a very common pattern:

• bona = good → malbona = bad
• granda = big → malgranda = small
• varma = warm → malvarma = cold

So la malpura ombrelo means the dirty umbrella.

Because these are prepositional phrases, and the prepositions antaŭ and apud already show the relationship.

Normally, nouns after prepositions do not take -n:

• antaŭ la pordo
• apud la lampo

The accusative after a preposition is mainly used when showing direction toward somewhere, not simple location. Here the sentence describes where things are, not movement toward a place.

They work differently:

• vidi = to see
  This verb takes a direct object.
  So in Mi vidas dormantan katon, katon is the object.

• kuŝi = to lie, to be lying
  This verb does not take a direct object.
  So in kuŝas la malpura ombrelo, la malpura ombrelo is the subject.

This is why one noun phrase has -n and the other does not.

Kaj means and. It connects two clauses:

• Mi vidas dormantan katon antaŭ la pordo
• apud la ŝaltita lampo kuŝas la malpura ombrelo

Using kaj makes the sentence flow as one combined description. Esperanto uses kaj very much like English uses and.

Yes. A more straightforward version would be:

Mi vidas dormantan katon antaŭ la pordo, kaj la malpura ombrelo kuŝas apud la ŝaltita lampo.

This means the same thing.

The original version is a bit more stylistic because it places apud la ŝaltita lampo first, which highlights the location before introducing the umbrella.

It can mean either, depending on how literally you want to think about it.

Grammatically, dormanta is a participial adjective, so it is very close to:

• a sleeping cat
• a cat that is sleeping

In normal translation, sleeping cat is the most natural English equivalent.

Because Esperanto present tense -as already covers the idea of is / am / are plus the verb in many English cases.

So:

• kuŝi = to lie
• kuŝas = lies / is lying

Similarly:

• dormas = sleeps / is sleeping
• vidas = see / sees, depending on the subject

English often chooses between simple and progressive forms, but Esperanto usually uses the plain tense form unless there is a special reason to be more explicit.