Ben arka kapıyı kapatıyorum.

Yes, you can usually leave ben out.

Turkish verbs already show the subject, and -um in kapatıyorum tells you the subject is I. So:

• Ben arka kapıyı kapatıyorum.
• Arka kapıyı kapatıyorum.

Both mean the same thing.

Including ben often adds emphasis, like:

• I’m closing the back door.
• Not someone else.

Because arka kapıyı is the specific direct object of the verb.

In Turkish, a specific/definite direct object usually takes the accusative ending. Here:

• kapı = door
• kapıyı = the door / the specific door

Since the sentence is about the back door, not just any back door, Turkish uses the accusative.

Compare:

• Arka kapı kapatıyorum. → not correct here
• Arka kapıyı kapatıyorum. → I am closing the back door

This happens because Turkish adds the accusative suffix to the noun.

The noun is:

• kapı = door

The accusative suffix here is:

• -ı

But Turkish usually inserts a buffer letter y when a suffix beginning with a vowel is added to a word that already ends in a vowel.

So:

• kapı + ı would be awkward
• Turkish makes it kapı + y + ı
• Result: kapıyı

This y does not add meaning; it just makes pronunciation smoother.

Kapatıyorum can be divided like this:

• kapat- = close, shut
• -ıyor- = present continuous
• -um = I

So:

• kapatıyorum = I am closing

Full sentence:

• Ben arka kapıyı kapatıyorum.
• I am closing the back door.

The present continuous in Turkish is built with -iyor / -ıyor / -üyor / -uyor, depending on vowel harmony.

The verb stem here is kapat-. The last vowel before the suffix is a, so the form becomes -ıyor.

So:

• kapat- + -ıyor + -um
• kapatıyorum

This is the Turkish tense most often used for am/is/are doing.

Its most natural meaning here is I am closing.

But Turkish -yor forms can sometimes also be used more broadly, depending on context, for things like:

• something happening right now
• something currently in progress
• sometimes a planned near future

In this sentence, though, the normal reading is:

• I am closing the back door

Because in Turkish, modifiers usually come before the noun they describe.

So:

• arka = back, rear
• kapı = door
• arka kapı = back door / rear door

This is very normal Turkish word order inside a noun phrase.

Because Turkish normally uses Subject–Object–Verb order.

So in this sentence:

• Ben = subject
• arka kapıyı = object
• kapatıyorum = verb

That gives:

• Ben arka kapıyı kapatıyorum.

English usually prefers Subject–Verb–Object:

• I am closing the back door.

Turkish is more flexible than English, but putting the verb at the end is the most neutral pattern.

Yes, kapatmak is a very common verb meaning to close or to shut.

You can use it for many things:

• kapıyı kapatmak = to close the door
• pencereyi kapatmak = to close the window
• televizyonu kapatmak = to turn off the television

So in this sentence, kapatıyorum is exactly what you would expect for I am closing/shutting.

Yes. Then the meaning becomes more general:

• Kapıyı kapatıyorum. = I am closing the door.

Adding arka makes it more specific:

• Arka kapıyı kapatıyorum. = I am closing the back door.

Turkish does not have separate words for a/an/the like English does.

Instead, things like specificity are often shown through grammar and context. In this sentence, kapıyı has the accusative ending, which strongly suggests a specific door:

• kapıyı = the door / that door

So even though Turkish does not use a word equivalent to the, the meaning is still there.

Learners may notice forms like kapıyorum, but for closing a door, kapatıyorum is the normal and expected form.

In everyday Turkish, kapatmak is the standard verb for to close/shut something like a door, window, or device.

So for this sentence, stick with:

• Ben arka kapıyı kapatıyorum.

That is the most natural choice.