Kapının dışı kirli.

Because kapının is the genitive form of kapı. The genitive often corresponds to English of the door or the door’s.

• kapı = door
• kapının = of the door / the door’s

In this sentence, Turkish is using a very common structure:

• X-in Y-si = the Y of X

So:

• kapının dışı = the outside of the door

The ending -ın is chosen because of vowel harmony and consonant rules.

Because in this construction, the second noun usually takes a possessive ending.

Here the pattern is:

• kapının = of the door
• dışı = its outside / outside part

So kapının dışı is literally something like the door’s outside.

Compare:

• dış = outside, exterior
• dışı = its outside / the outside of it

This is a standard Turkish noun phrase pattern called the genitive-possessive construction.

It is a possessive noun phrase, often called the genitive-possessive construction.

The pattern is:

• first noun: genitive
• second noun: 3rd person possessive

So:

• kapının = of the door
• dışı = its outside

Together:

• kapının dışı = the outside of the door

This same pattern appears in many common expressions:

• evin kapısı = the door of the house
• arabanın rengi = the color of the car
• masanın üstü = the top of the table

It is one of the most important noun patterns in Turkish.

In Turkish, the verb to be is often not expressed in simple present-tense sentences like this.

So:

• Kapının dışı kirli. literally looks like The door’s outside dirty.
• But it naturally means The outside of the door is dirty.

This is completely normal in Turkish.

You also see the same thing in sentences like:

• Ev büyük. = The house is big.
• O mutlu. = He/She is happy.

If you want the past tense or other forms, Turkish does add endings or words:

• Kapının dışı kirliydi. = The outside of the door was dirty.
• Kapının dışı kirli değil. = The outside of the door is not dirty.

Because kirli is the predicate adjective here.

In English, we say:

• The outside of the door is dirty.

In Turkish, the thing being described usually comes first, and the description comes after it:

• Kapının dışı = the outside of the door
• kirli = dirty

So the sentence structure is basically:

• subject + description

This is very common in Turkish:

• Çay sıcak. = The tea is hot.
• Oda temiz. = The room is clean.
• Kapının dışı kirli. = The outside of the door is dirty.

In this sentence, it means the exterior / outer side of the door, not the area beyond the door.

That is an important distinction.

• kapının dışı = the outside surface or outer part of the door
• kapının dışında = outside the door / on the outside of the door

So:

• Kapının dışı kirli. = The door’s outer side is dirty.
• Kapının dışında bekliyorum. = I am waiting outside the door.

The ending matters a lot here:

• dışı = its outside
• dışında = on/outside of it

Not in standard Turkish for this meaning.

To say the outside of the door, Turkish normally wants the full possessive structure:

• kapının dışı

If you say kapı dışı, it does not sound like a normal way to express the outside of the door.

So for learners, the safe and correct form is:

• Kapının dışı kirli.

This is because Turkish strongly prefers the genitive-possessive pattern for relationships like the X of Y.

Use değil for the negative, and mi for a yes/no question.

• Kapının dışı kirli değil. = The outside of the door is not dirty.
• Kapının dışı kirli mi? = Is the outside of the door dirty?

You can also combine them:

• Kapının dışı kirli değil mi? = Isn’t the outside of the door dirty?

This is very useful because adjective sentences in Turkish do not use a separate present-tense is, so negation is usually done with değil.

The Turkish ı is a very important vowel because it does not exist in standard English.

It is:

• not the same as i
• a back, unrounded vowel

A rough approximation is the vowel sound in the second syllable of sofa for some speakers, but that is only approximate.

So:

• kapı sounds roughly like kah-puh
• dışı sounds roughly like duh-shuh

But those are only guides. The key point is:

• i = like ee in many cases
• ı = a different vowel, more central/back and unrounded

This contrast changes meaning in Turkish, so it is worth practicing carefully.

Because this is the 3rd person singular possessive suffix, and after many consonant-final nouns it appears as one of these forms:

• -ı
• -i
• -u
• -ü

Which one appears depends on vowel harmony.

Since dış contains the vowel ı, the matching possessive ending is also -ı:

• dış
  • -ı → dışı

Similarly:

• ev → evi
• yol → yolu
• göz → gözü

So dışı means its outside or the outside of it.

Turkish can do this with many nouns. It is a very productive pattern.

Examples:

• arabanın önü = the front of the car
• evin arkası = the back of the house
• kutunun içi = the inside of the box
• masanın üstü = the top of the table
• kapının kolu = the handle of the door

So kapının dışı is not just a memorized phrase. It follows a broad grammatical pattern that you will see everywhere in Turkish.