Kedinin tüyleri koltuğa yapışınca kılıfı yıkadım.

Because kedinin has the genitive ending -in, which marks the possessor.

• kedi = cat
• kedinin = the cat’s

In Turkish, possession is usually shown with a two-part structure:

• the possessor gets the genitive
• the possessed noun gets a possessive ending

So:

• kedinin tüyleri = the cat’s fur/hairs

This is a very common Turkish pattern.

Because the two expressions are similar but not identical.

• kedi tüyleri = cat hair/fur in a more general sense, like cat hairs
• kedinin tüyleri = the fur/hairs of a specific cat

In this sentence, we are talking about hair from a particular cat, so kedinin tüyleri is the better choice.

Because the noun being possessed must also show possession.

• tüyler = hairs/fur
• tüyleri = its hairs / the cat’s hairs

Here, tüyleri contains:

• tüy = hair, fur, feather
• -ler = plural
• -i = 3rd person possessive

So kedinin tüyleri literally works like the cat’s its-hairs, which is how Turkish builds the cat’s fur/hair.

As for tüyü, that would be singular possessed: its hair/feather. But in a sentence about loose hair sticking to furniture, tüyleri sounds very natural.

Yes, it is grammatically plural here, but English and Turkish do not always package this idea the same way.

Turkish often uses a plural form when thinking about many separate hairs or strands:

• tüyleri = its hairs

But natural English may prefer:

• the cat’s fur
• the cat’s hair

So the Turkish form can be plural even when the best English translation sounds singular.

Because yapışmak takes the dative case, meaning to stick to something.

• koltuk = sofa, armchair, seat
• koltuğa = to the sofa / to the chair

So:

• koltuğa yapışmak = to stick to the sofa

A learner might expect koltukta, but that would mean on/in the sofa as a location, not the target of sticking.

Also notice the sound change:

• koltuk + a → koltuğa

The final k softens to ğ before a vowel-initial suffix.

Yapışınca comes from:

• yapış- = stick, adhere
• -ınca / -ince = when, once, after, sometimes because

So yapışınca means something like:

• when it stuck
• once it stuck
• after it stuck

Depending on context, it can even feel a bit like since/because it stuck.

In this sentence, it introduces the background event: When the cat’s fur stuck to the sofa, I washed the cover.

Because these are different verbs.

• yapışmak = to stick, to become attached
• yapıştırmak = to make something stick, to stick something onto something

So:

• Tüyler koltuğa yapıştı. = The hairs stuck to the sofa.
• Tüyleri koltuğa yapıştırdı. = He/she stuck the hairs onto the sofa.

In your sentence, the fur is the thing that got stuck by itself, so yapışmak is correct.

Here -ı is the accusative ending, marking a definite/specific direct object.

• kılıf = cover
• kılıfı = the cover

So:

• kılıfı yıkadım = I washed the cover

Turkish often marks direct objects this way when they are specific or already known from context.

Compare:

• kılıfı yıkadım = I washed the cover
• bir kılıf yıkadım = I washed a cover

Yes, by itself kılıfı can be ambiguous.

It can look like:

• kılıf + ı = the cover, as an accusative object or
• a possessed form meaning its cover

But in this sentence, it is normally understood as the cover.

If you wanted to say its cover as the object more clearly, Turkish would often use:

• kılıfını = its cover + accusative

And if you wanted to be very explicit:

• koltuğun kılıfını = the sofa’s cover

Yıkadım breaks down like this:

• yıka- = wash
• -dı = past tense
• -m = first person singular

So:

• yıkadım = I washed

This is one reason Turkish often does not need a separate subject pronoun.

Because the verb already tells you the subject.

In yıkadım, the ending -m means I.

So Turkish can simply say:

• yıkadım = I washed

You can add ben if you want emphasis or contrast:

• Ben yıkadım. = I washed it.

But in an ordinary sentence, the pronoun is usually omitted.

Not completely, but the given order is very natural.

The sentence is arranged as:

1. subordinate clause
2. object
3. main verb

So:

• Kedinin tüyleri koltuğa yapışınca kılıfı yıkadım.

This is a normal Turkish pattern.

Turkish word order is flexible, so parts can move for emphasis. For example:

• Kılıfı, kedinin tüyleri koltuğa yapışınca yıkadım.

That still means roughly the same thing, but puts more focus on kılıfı.

The main verb usually stays near the end.