Learn Hardcore Japanese: hondana no ue ni neko ga iru. - There is a cat on top of the bookshelf.

Without の, 本棚上 is not natural modern Japanese. In structures like Noun + の + Noun, the の is needed to show the relationship between the two nouns.

Is 上 (うえ) a preposition like “on,” or is it something else?

上 is a noun, not a preposition.

It means “top,” “upper part,” “above,” “on (top)” as a location noun.
To turn it into “on / on top of” in the sentence, Japanese uses:
- 本棚の上に → literally “at the top of the bookshelf”
  (location noun + particle に)

So instead of a preposition like English on, Japanese typically uses:

location noun (上, 中, 前, 後ろ, 右, 左, etc.)
plus a particle (usually に or で)
often linked with の to another noun (本棚の上, 机の下, etc.).

Why do we use に after 上? What does に do here?

In 本棚の上に猫がいる, に marks the location where something exists.

With the verb いる / ある (to exist / there is), the pattern is:

[Place] + に + [thing/person] + が + いる / ある

So:

本棚の上に = on top of the bookshelf (as a place)
猫がいる = a cat exists / there is a cat

Together: “On top of the bookshelf, there is a cat.”

Use に when:

You’re stating the existence of something in a place (not describing an action taking place there).

What’s the difference between に and で for locations? Could I say 本棚の上で猫がいる?

に and で both relate to location, but they have different typical uses:

に → location of existence or state
- 本棚の上に猫がいる。
  There is a cat on top of the bookshelf.
- 部屋に人がいる。
  There are people in the room.
で → location of an action / event
- 本棚の上で猫が寝ている。
  The cat is sleeping on top of the bookshelf.
- 部屋で勉強する。
  I study in the room.

With いる / ある, you almost always use に, not で.
So 本棚の上で猫がいる sounds wrong or at least very unnatural.

Why is 猫 marked with が instead of は?

In 猫がいる, が marks the grammatical subject and often highlights what exists / appears / is noticed.

In existence sentences like this, が is the default:

本棚の上に猫がいる。
There is a cat on top of the bookshelf. (We’re introducing the cat.)

は marks the topic, often meaning “as for…” and usually presumes the listener already knows what we’re talking about:

猫は本棚の上にいる。
The cat, as for it, is on top of the bookshelf.

So:

Use が when introducing or focusing on the existence of something.
Use は when you’re talking about something already established as the topic.

Can I say 猫は本棚の上にいる instead? What’s the nuance difference?

Yes, 猫は本棚の上にいる is perfectly correct, but the nuance changes.

本棚の上に猫がいる。

Neutral translation: There is a cat on top of the bookshelf.
Focus: “What is there on top of the bookshelf?” → “A cat is there.”
Often used to introduce the cat.

猫は本棚の上にいる。

Neutral translation: The cat is on top of the bookshelf.
Focus: “Where is the cat?” → “It’s on top of the bookshelf.”
The cat is the topic; we’re stating its location.

So they are both grammatical, but they answer different implicit questions:

が version: answers “What is there?”
は version: answers “Where is it?”

What’s the difference between いる and ある? When should I use which?

Both mean “to exist / there is / there are”, but:

いる → for living / animate things
- people, animals (including a cat), sometimes personified characters
- 猫がいる。 There is a cat.
- 人がいる。 There is a person.
ある → for inanimate things
- objects, places, abstract things, events, etc.
- 本がある。 There is a book.
- 公園がある。 There is a park.

Some notes:

Plants are usually treated as ある (inanimate) in everyday speech.
Robots, characters, spirits, etc. can vary depending on whether they’re being thought of as “living” or just as objects in context.

In your sentence, 猫 is an animal, so いる is correct: 猫がいる。

Is the word order fixed? Could I say 猫が本棚の上にいる instead?

Japanese word order is relatively flexible, as long as:

The particles stay attached to the right words.
The verb (いる) comes at the end (in neutral style).

These are all natural and mean essentially the same thing:

本棚の上に猫がいる。
猫が本棚の上にいる。

The difference is mostly in focus / emphasis and flow of information:

Starting with 本棚の上に puts more initial focus on the location.
Starting with 猫が puts more initial focus on the cat.

But grammatically both are fine because:

に still marks the place
が still marks the subject
いる is still the final verb.

Where is “a” or “the” in this Japanese sentence? How do I know if it’s “a cat” or “the cat”?

Japanese does not have articles like “a/an” or “the”.
Whether it’s “a cat” or “the cat” is decided by context, not by a specific word.

If you are mentioning the cat for the first time, English will usually use “a cat”:
- 本棚の上に猫がいる。 → There is a cat on top of the bookshelf.
If both speaker and listener already know which cat you mean (maybe you have only one cat), English may use “the cat”:
- (We’re looking for your cat.)
  本棚の上に猫がいる。 → The cat is on top of the bookshelf.

So Japanese 猫 is neutral; you choose a or the in English depending on the situation.

How do I make this sentence polite, or negative, or past tense?

The core verb いる behaves like a regular る-verb.

Polite present
- 本棚の上に猫がいます。
  There is a cat on top of the bookshelf. (polite)
Negative (plain / polite)
- 本棚の上に猫がいない。 (plain)
- 本棚の上に猫がいません。 (polite)
  → There is no cat on top of the bookshelf.
Past (plain / polite)
- 本棚の上に猫がいた。 (plain)
- 本棚の上に猫がいました。 (polite)
  → There was a cat on top of the bookshelf.

The rest of the sentence (本棚の上に猫が) stays the same; you just change the form of いる.