Dit kontor er lyst, men mit er roligt.

Because kontor is a neuter noun in Danish: et kontor.

Danish possessives change to match the gender and number of the noun they describe:

• min / din / sin for common gender singular nouns
• mit / dit / sit for neuter singular nouns
• mine / dine / sine for plurals

So:

• en bil → din bil
• et kontor → dit kontor

That is why the sentence has dit kontor.

Here mit stands on its own and means my one / mine, referring back to kontor.

So:

• Dit kontor er lyst, men mit er roligt means
• Your office is bright, but mine is quiet/calm

The full version would be:

• Dit kontor er lyst, men mit kontor er roligt

Danish often leaves out a repeated noun when it is already clear from context.

Because the adjectives agree with the noun kontor, which is neuter.

In this sentence, the adjectives are used after er, so they are predicative adjectives, but they still agree in gender and number:

• common gender singular: lys, rolig
• neuter singular: lyst, roligt
• plural: lyse, rolige

Since kontor is neuter:

• kontoret er lyst
• mit kontor er roligt

So the -t ending is there because the thing being described is et kontor.

In this context, lyst usually means bright or light, especially about a room, office, or space.

It can suggest things like:

• a lot of natural light
• a bright atmosphere
• light colors

So for a room or office, lyst is often best understood as bright rather than the English idea of light as the opposite of heavy.

Here roligt means something like:

• calm
• quiet
• peaceful

About an office, it usually suggests a quiet or peaceful environment, not one with a lot of noise or activity.

A useful warning: if you know Swedish, Swedish rolig means funny/fun, but in Danish rolig means calm/quiet.

Because the sentence contains two full clauses joined by men:

• Dit kontor er lyst
• mit er roligt

Each clause needs its own verb, and here the verb is er in both clauses.

So Danish does not normally say:

• Dit kontor er lyst, men mit roligt

Instead, it keeps the verb:

• Dit kontor er lyst, men mit er roligt

Men means but. It joins two main clauses.

After men, the second clause keeps normal main-clause word order:

• subject + verb: mit er roligt

So men itself does not force inversion here. The second part is simply another main clause.

Because men connects two separate clauses, each with its own finite verb:

• er in Dit kontor er lyst
• er in mit er roligt

A comma before men is standard in a sentence like this.

Yes, absolutely.

That version is completely correct. It just repeats kontor instead of leaving it understood.

The shorter version:

• Dit kontor er lyst, men mit er roligt

is more natural when the noun is already obvious.

So both are correct:

• Dit kontor er lyst, men mit er roligt
• Dit kontor er lyst, men mit kontor er roligt

The shorter one sounds smoother and less repetitive.

Yes, in this sentence it works like English mine.

But the important difference is that Danish changes form depending on the noun behind it:

• min if the omitted noun is common gender singular
• mit if the omitted noun is neuter singular
• mine if the omitted noun is plural

So here it is mit because the hidden noun is kontor, and kontor is neuter:

• mit = my office / mine