Después de cenar, prefiero un té de menta.

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Breakdown of Después de cenar, prefiero un té de menta.

• un: a
• después de: after
• cenar: to have dinner

Questions & Answers about Después de cenar, prefiero un té de menta.

Why is it después de cenar and not just después cenar?

Because después normally needs the preposition de before a noun or an infinitive.

• después de cenar = after having dinner / after dinner
• después de la cena = after the dinner / after dinner

So de is required here.
A very common pattern is:

• después de + noun
• después de + infinitive

Examples:

• después de comer = after eating / after lunch
• después de trabajar = after working

Why is cenar in the infinitive instead of something like después de ceno?

After después de, Spanish uses the infinitive when the subject is general or understood.

So:

• después de cenar = after eating dinner / after dinner

You do not use a conjugated verb like ceno here.

Compare:

• Después de cenar, salgo. = After dinner, I go out.
• Después de trabajar, descansamos. = After working, we rest.

This is very natural in Spanish and often matches English structures like after eating, after working, etc.

What exactly does cenar mean? Is it to eat or to have dinner?