Det lilla skåpet i hallen är låst, och det är förbjudet att lägga nyckeln där.

Because skåp is an ett-word in Swedish:

• ett skåp = a cabinet / a cupboard
• skåpet = the cabinet / the cupboard

When an ett-word is definite and also has an adjective, Swedish usually uses this pattern:

• det + adjective + noun with definite ending

So:

• det lilla skåpet = the small cabinet

A few parts are working together here:

• det = definite article used with neuter nouns
• lilla = definite form of liten (small)
• skåpet = skåp
  • -et, the definite ending for this noun

Den would be used with a common-gender noun (en-word), not with skåp.

Swedish adjectives change form depending on gender, number, and definiteness.

For liten:

• en liten nyckel = a small key
• ett litet skåp = a small cabinet
• små nycklar/skåp = small keys/cabinets
• det lilla skåpet = the small cabinet

In definite phrases, liten usually becomes lilla regardless of gender:

• den lilla bilen
• det lilla skåpet
• de lilla barnen

So lilla here is the normal definite form.

Yes, in a sense. Swedish often puts the definite article at the end of the noun as a suffix.

• ett skåp = a cabinet
• skåpet = the cabinet

So -et is the definite ending for this neuter noun.

Then when there is also an adjective, Swedish often uses a “double definite” structure:

• det lilla skåpet

That literally looks a bit like the small the-cabinet from an English perspective, but it is normal Swedish grammar.

Because hallen means the hall / the hallway, and in this sentence a specific hall is meant.

• en hall = a hall / hallway
• hallen = the hall / hallway

So:

• i hallen = in the hall / in the hallway

Swedish often uses the definite form for places when the location is specific and known from context, just as English often says in the hall rather than in hall.

Because låst is an adjective-like form meaning locked, while låset would be the noun the lock.

Compare:

• låst = locked
• ett lås = a lock
• låset = the lock

So:

• skåpet är låst = the cabinet is locked

Here låst describes the state of the cabinet, just like English locked in is locked.

In this sentence, it functions like an adjective describing a state.

• låsa = to lock
• låst = locked

So är låst means is locked.

Historically and grammatically, låst comes from the past participle of låsa, but for a learner it is often easiest to think of it here as a predicate adjective: it describes the condition of the cupboard.

This det is an impersonal or dummy subject, similar to English it in expressions like:

• It is forbidden to smoke
• It is important to leave early

Swedish does the same thing:

• det är förbjudet att ... = it is forbidden to ...

So the second det does not mean the cupboard. It is just the grammatical subject required in this type of sentence.

Compare the two det forms in the full sentence:

• Det lilla skåpet = The small cupboard
• det är förbjudet att ... = it is forbidden to ...

They look the same, but they have different roles.

Förbjudet means forbidden.

It comes from förbjuda = to forbid.

In det är förbjudet att lägga nyckeln där, it works like an adjective in a fixed expression:

• det är förbjudet att ... = it is forbidden to ...

You can think of it as parallel to:

• det är viktigt att ... = it is important to ...
• det är svårt att ... = it is difficult to ...

So the structure is very common in Swedish.

Because att lägga is the infinitive, meaning to put / to place / to lay.

In Swedish, after expressions like det är förbjudet, you normally use att + infinitive:

• det är förbjudet att röka = it is forbidden to smoke
• det är förbjudet att parkera här = it is forbidden to park here
• det är förbjudet att lägga nyckeln där = it is forbidden to put the key there

So att here is the infinitive marker, like English to.

Swedish often distinguishes placement verbs more specifically than English does.

• lägga = put/lay something so that it lies down
• ställa = put/set something so that it stands
• sätta = put/set something in a sitting position, or sometimes place something onto a surface/in a spot

For a nyckel (key), lägga is very natural, because a key is normally thought of as lying down when placed somewhere.

So:

• lägga nyckeln där = put the key there

English uses put for many situations where Swedish chooses among several verbs.

Because nyckeln means the key, a specific key already known from the situation.

• en nyckel = a key
• nyckeln = the key

In this sentence, it is not talking about any random key; it means a particular key, so the definite form is used.

Där means there.

It refers to a place already understood from context. In this sentence, the most natural reading is that it refers to the place just mentioned or implied by the discussion of the cupboard in the hall.

So:

• lägga nyckeln där = put the key there

Swedish often uses där exactly like English there when the location does not need to be repeated.

This is standard Swedish main-clause word order:

• subject: Det lilla skåpet i hallen
• verb: är
• predicate/adjective: låst

So literally:

• The small cupboard in the hall
  • is
    • locked

The phrase i hallen comes right after skåpet because it describes which cupboard is meant: the one in the hall.

It most naturally describes skåpet:

• Det lilla skåpet i hallen = The small cupboard in the hall

So the phrase identifies which cupboard we are talking about.

If Swedish wanted to emphasize location more as part of the whole situation, other word orders might be possible in different contexts, but here the most natural interpretation is simply that the cupboard is located in the hall.

Yes. Skåp is a fairly broad word and can mean:

• cupboard
• cabinet
• locker
• sometimes closet-like storage furniture, depending on context

The exact English translation depends on what kind of object is meant. In your sentence, cupboard or cabinet both work well.

The comma is possible because the sentence joins two full clauses:

• Det lilla skåpet i hallen är låst
• det är förbjudet att lägga nyckeln där

In Swedish, punctuation around och is often a bit lighter than in English, and many writers would also omit the comma here. So the comma is not the most important part of the grammar; it is mainly a punctuation choice that helps separate the two clauses.

Yes. That would also be normal.

Both versions can occur:

• ... är låst, och det är förbjudet ...
• ... är låst och det är förbjudet ...

The meaning does not change. The comma just adds a clearer pause between the two clauses.

Yes, very common.

This pattern is useful and productive:

• det är förbjudet att + infinitive
• det är tillåtet att + infinitive
• det är viktigt att + clause/infinitive
• det är svårt att + infinitive

Examples:

• Det är förbjudet att röka här. = It is forbidden to smoke here.
• Det är förbjudet att parkera här. = It is forbidden to park here.
• Det är förbjudet att lägga nyckeln där. = It is forbidden to put the key there.

So this sentence is a good example of a very useful structure to learn.