Després de dinar, m'agrada estirar-me al sofà amb un coixí petit.

Because després de + infinitive is a very common way to say after doing something.

• després de dinar = after having lunch / after eating lunch
• després del dinar = after the lunch / after lunch as a specific meal or event

Both can be possible, but they are not exactly the same structure. In your sentence, Catalan is focusing on the action to have lunch, so the infinitive dinar is natural.

Here it is a verb in the infinitive: to have lunch.

That can be confusing because dinar can also be a noun meaning lunch. Catalan often uses the same form for a noun and an infinitive.

In this sentence, you can tell it is verbal because it comes after després de, which often introduces an infinitive:

• després de dinar = after having lunch

If it were the noun, you would normally expect an article:

• després del dinar = after lunch / after the meal

Literally, m'agrada means it pleases me.

Catalan uses agradar differently from English to like:

• English: I like lying on the sofa
• Catalan structure: Lying on the sofa pleases me

So:

• m' = to me
• agrada = is pleasing

That is why the person who likes something is not the grammatical subject in the same way as in English.

Because the thing being liked is the whole infinitive phrase estirar-me al sofà amb un coixí petit, and that whole idea is treated as singular.

So:

• M'agrada estirar-me... = I like lying/stretching out...

Compare:

• M'agrada llegir. = I like reading.
• M'agrada descansar. = I like resting.

But with a plural noun, you would use agraden:

• M'agraden els coixins petits. = I like small pillows.

Because the verb is estirar-se, a reflexive/pronominal verb here, and with an infinitive the pronoun is normally attached to the end.

So:

• estirar-se = to stretch out / to lie down
• estirar-me = to stretch out / lie down myself

Compare:

• m'estiro = I stretch out / lie down
• estirar-me = to stretch out / lie down

This is a very common pattern in Catalan:

• rentar-se = to wash oneself
• rentar-me = to wash myself
• asseure's = to sit down
• asseure'm = to sit down myself

In this sentence, it means something like to stretch out, to lie down, or to recline on the sofa.

The basic idea of estirar is to stretch. But estirar-se often means stretching oneself out physically, especially on a bed or sofa.

So here it is not just a quick physical stretch like after exercise. It suggests relaxing by lying back comfortably.

Al is the contraction of a + el.

• a = to / at / on, depending on context
• el sofà = the sofa
• al sofà = on the sofa / on the couch

In English we usually say on the sofa, but Catalan commonly uses a in this kind of expression.

So:

• al sofà = literally at/to the sofa, but naturally on the sofa

Amb means with.

Here it shows accompaniment or something you have with you while doing the action:

• amb un coixí petit = with a small pillow

So the sentence describes how the person likes to lie on the sofa: they do it with a small pillow.

In Catalan, adjectives often come after the noun in the most neutral, everyday order.

So:

• un coixí petit = a small pillow

That is the most straightforward descriptive order.

You can sometimes place an adjective before the noun, but that often adds emphasis, style, or a slightly different nuance. For a simple factual description, coixí petit is the normal choice.

Also notice agreement:

• coixí is masculine singular
• so the adjective is also masculine singular: petit

Because coixí is a masculine noun in Catalan.

So you use:

• un coixí
• el coixí
• coixí petit

If the noun were feminine, you would use:

• una
• la
• and a feminine adjective form, such as petita

For example:

• una manta petita = a small blanket

Because Després de dinar is an introductory time expression placed at the beginning of the sentence.

The comma helps separate that opening phrase from the main clause:

• Després de dinar, m'agrada...

In short sentences, punctuation can sometimes be a bit flexible, but this comma is very natural and helps readability.

Yes. Catalan word order is fairly flexible, especially with time expressions.

For example, you could also say:

• M'agrada estirar-me al sofà amb un coixí petit després de dinar.

That still sounds natural. The version with Després de dinar at the beginning gives a little more emphasis to the time frame, as in After lunch, ...