Nec mater nec pater domi adest.

It means neither ... nor.

So Nec mater nec pater domi adest means that mother is not at home, and father is not at home either. Latin often repeats nec before each item being linked.

Yes. Nec is essentially a shorter form of neque.

Both can mean and not, and when used in a pair, nec ... nec or neque ... neque means neither ... nor. For a beginner, they can usually be treated as equivalent in sentences like this.

They are both nominative singular.

They are in the nominative because they are the subjects of the verb adest. In other words, they are the ones being said to be absent from home.

Also, both mater and pater are third-declension nouns, even though they end in -er.

Latin does not have articles like English the or a.

So mater can mean:

• mother
• the mother
• my mother

The exact meaning depends on context.

With family words, Latin also often leaves out a possessive word where English might naturally use one. So a learner should not be surprised if mater and pater are used without mea or meus.

Because Latin can treat nec ... nec with singular nouns distributively, meaning each one separately.

So the sense is:

• neither mother is present
• nor father is present

That is why singular adest is natural here. In some Latin sentences a plural verb may appear with two coordinated subjects, but the singular in this pattern is very common and idiomatic.

Adest is the third-person singular present form of adesse.

Adesse is a compound of ad- and esse / sum, and it means:

• to be present
• to be here
• to be near
• sometimes to be available

So adest means he/she/it is present. In this sentence, it fits the idea is at home or is present at home.

Because adest is more specific than est.

• est = is
• adest = is present / is here

So adest emphasizes presence. In English, we may simply translate the sentence as Neither mother nor father is at home, but Latin uses adest to express the idea of being present there.

Because domi is the normal idiomatic Latin way to say at home.

It is a special form called the locative, used for place where something is. With domus, Latin often uses:

• domi = at home
• domum = homeward / to home
• domo = from home

By contrast, in domo means more literally in the house. That focuses more on the building itself, while domi means at home in the usual everyday sense.

Domi is locative.

The locative is an old case used mainly for place where. Latin mostly lost it as a separate case, but it survives in a few important words, especially:

• names of towns and cities
• domi from domus

So here domi answers the question where? — at home.

Latin word order is much more flexible than English word order.

This sentence puts nec mater nec pater first, so the two contrasted subjects are presented right away, and then places adest at the end, which is very common in Latin.

The basic meaning would stay the same even if the words were rearranged, but the emphasis could change. Latin word order often helps show what the writer wants to highlight, not just the grammatical relationships.