Pumpička je vedle sady lepení.

Because vedle requires the genitive case.

The basic dictionary form is sada.
After vedle, it changes to sady:

• sada = nominative singular
• sady = genitive singular

So:

• vedle sady = next to the kit/set

This is very common in Czech: prepositions often force a specific case.

Here, lepení is a verbal noun based on the verb lepit = to glue / to patch.

So sada lepení is a compact way of saying something like a kit for patching/gluing.

It is also in the genitive singular after sady, because sada often takes a dependent noun in the genitive:

• sada nářadí = a set of tools
• sada klíčů = a set of keys

With lepení, the form happens to look the same in several cases, so lepení stays lepení.

A very common learner question. In Czech, you cannot guess the case only from the meaning location. You have to learn which case each preposition governs.

For example:

• v
  • locative: v domě = in the house
• na
  • locative: na stole = on the table
• vedle
  • genitive: vedle domu = next to the house

So even though vedle describes location, it still takes the genitive, not the locative.

Yes, pumpička is a diminutive form related to pumpa.

In practice, pumpička often means a small pump, especially a hand pump or bicycle pump. Diminutives in Czech are extremely common and do not always sound childish or overly cute. Very often they are just the normal everyday word for a smaller object.

So pumpička can sound more natural than a plain pumpa if you mean a small portable pump.

Because Czech has no articles.

English needs words like a and the, but Czech usually leaves that information to context.

So Pumpička je vedle sady lepení can mean:

• The pump is next to the patch kit
• A pump is next to a patch kit

The exact interpretation depends on the situation.

If Czech speakers want to be more specific, they can use other words such as ta, ten, jedna, etc., but there is no direct article system like in English.

Yes. Czech word order is fairly flexible.

For example, you could also say:

• Vedle sady lepení je pumpička.

That is still grammatical. The difference is mainly emphasis or information structure:

• Pumpička je vedle sady lepení.
  Starts with pumpička as the topic.

• Vedle sady lepení je pumpička.
  Starts with the location, so it feels more like Next to the patch kit, there is a pump.

Because Czech marks relationships with cases, word order is often freer than in English.

It is understandable, but many speakers might also say something more explicit, such as:

• sada na lepení
• lepicí sada

The version in your sentence uses a compact noun phrase: sada + a dependent noun. That structure is normal in Czech, but with lepení, some learners may hear sada na lepení more often in everyday speech.

So the sentence is workable, but it is good to know there are alternative ways to phrase it.

A simple guide:

• Pumpička = PUM-pich-ka
• je = ye
• vedle = VED-le
• sady = SA-dy
• lepení = LE-pe-nee

A few useful pronunciation points:

• č sounds like ch in church
• í is a long ee sound
• Czech stress usually falls on the first syllable of each word

So the whole sentence sounds roughly like:

PUM-pich-ka ye VED-le SA-dy LE-pe-nee

The nouns are:

• pumpička — feminine
• sada — feminine
• lepení — neuter

Gender always matters in Czech, because it affects adjective endings, pronouns, and past tense forms.

In this sentence, gender is not very visible because:

• je is the same for all genders in the present tense
• there are no adjectives modifying the nouns

But if you added an adjective, gender would show up clearly:

• malá pumpička = small pump
• malá sada = small kit
• malé lepení = small patching/gluing activity/material

So yes, gender matters, even if it is not the main thing you notice in this sentence.