В кафе мы взяли горячее какао, чтобы согреться после катка.

В кафе means in / at the café.

Here в is used with the prepositional case to show location.
Normally, a noun after в changes form in the prepositional, but кафе is one of those Russian nouns that is indeclinable, so it stays кафе in all cases.

So:

• в кафе = in the café / at the café

A learner may expect a visible case ending, but there is none here because кафе does not change.

Yes, взяли literally comes from взять, meaning to take. But in Russian, взять is also commonly used in situations where English would say:

• got
• ordered
• had

So in a café context, мы взяли горячее какао can naturally mean:

• we got hot cocoa
• we ordered hot cocoa
• we had hot cocoa

It does not necessarily mean physically picking something up with your hands. It often just means obtaining or choosing something.

This is an aspect question.

• взять = perfective
• брать = imperfective

Взяли is the past plural of the perfective verb взять, and it presents the action as a completed whole: we got / ordered the cocoa.

That fits the sentence well because it refers to one completed action in the story.

If you used брали, it would sound more like:

• we used to get
• we were getting
• we would get

So взяли is the natural choice for a single completed event.

Because какао is treated as neuter in Russian, so the adjective must agree with it.

• masculine: горячий
• feminine: горячая
• neuter: горячее

So:

• горячее какао = hot cocoa

Even though какао ends in -о, which often suggests neuter, it is also an indeclinable noun, so learners sometimes hesitate. But the adjective clearly shows the gender here: горячее tells you the noun is being treated as neuter.

Какао is an indeclinable noun. That means it usually keeps the same form in all cases.

So you can get forms like:

• какао
• горячее какао
• чашка какао
• после какао

and the word какао itself stays the same.

This is common with some borrowed words in Russian, especially words like:

• кафе
• метро
• пальто
• какао

The case and role in the sentence are usually shown by the surrounding words, prepositions, or adjectives.

Чтобы introduces a purpose clause. It means something like:

• in order to
• so that

So:

• чтобы согреться = in order to warm up / so that we could warm up

The sentence structure is very common in Russian:

• main action + чтобы
  • purpose

Examples:

• Я пришёл, чтобы помочь. = I came to help.
• Мы купили чай, чтобы согреться. = We bought tea to warm up.

Again, this is mainly about aspect.

• греться = to be warming oneself / to warm oneself up (process)
• согреться = to get warm / to warm oneself up successfully (result)

After чтобы, Russian often uses the verb that best expresses the intended result.

Here the point is not just the process of warming up, but the goal: to get warm after the skating rink. That is why согреться is natural.

So:

• чтобы греться would sound odd here
• чтобы согреться = to get warm

The ending -ся makes the verb reflexive, but reflexive verbs in Russian do not always translate literally as oneself in English.

Here согреться means:

• to get warm
• to warm oneself up

It describes a change in the subject’s own state. The people are doing something so that they themselves become warm.

Many Russian verbs with -ся are best learned as whole vocabulary items, because English may translate them in different ways.

Because the preposition после requires the genitive case.

The base form is:

• каток = skating rink

After после, it changes to the genitive singular:

• после катка = after the skating rink / after the time at the skating rink

This is a very important pattern:

• после работы = after work
• после урока = after the lesson
• после фильма = after the movie
• после катка = after the skating rink

In natural English, we usually would not say after the skating rink, but rather after going to the skating rink or after the skating session. Russian often uses the place noun this way.

It most naturally means after the skating-rink outing / after being at the rink.

Russian often uses a location noun to stand for the whole activity associated with that place. So после катка is understood as:

• after going to the skating rink
• after skating
• after our time at the rink

It does not have to mean the exact moment of physically leaving the building. It refers more generally to the period following that activity.

Russian word order is more flexible than English word order.

Both of these are possible:

• В кафе мы взяли горячее какао...
• Мы взяли горячее какао в кафе...

Starting with В кафе gives the setting first: As for the café / In the café... It helps frame the situation before the main action.

Russian often moves information around for emphasis, topic, or style rather than because grammar absolutely requires one order. The meaning stays basically the same, but the focus shifts slightly.

Yes, горячее какао is the direct object of взяли.

In Russian, direct objects are often in the accusative case. But here there is no visible change because:

1. какао is indeclinable, so it stays какао
2. the adjective горячее has the same form for nominative neuter singular and accusative neuter singular

So although it is grammatically the object, it looks the same as the basic dictionary form.

That is why this part can seem deceptively simple: the case is there grammatically, but you do not see much surface change.