Learn Hardcore Czech: Na dveřích knihovny je velký text „Otevřeno od devíti do pěti“. - On the library door there is a big text “Open from nine to five”.

na + locative (lokál): on, at – static location
- Na dveřích je nápis. – There is a sign on the door.
na + accusative (akuzativ): onto, to – movement/direction
- Nalepím to na dveře. – I’ll stick it onto the door.

In your sentence there is no movement; we are talking about where the text is. So Czech uses na + locative → na dveřích (on the door), not na dveře (onto the door).

What is going on with the word dveřích – why does door look plural and why this ending?

In Czech, dveře (door) is a plural‑only noun, like trousers or scissors in English. Even one door is grammatically plural:

nominative plural: dveře – door / doors
accusative plural: dveře
locative plural: dveřích – on/at the door(s)
genitive plural: dveří

Because na (in the sense on) requires the locative, you get na dveřích (on the door), literally on the doors.

Why is it knihovny and not knihovna or knihovně?

Knihovna (library) is a regular feminine noun:

nominative singular: knihovna – a/the library
genitive singular: knihovny – of the library
locative singular: knihovně – in/at the library

In na dveřích knihovny, the structure is:

dveře knihovny – the door(s) of the library
na dveřích knihovny – on the door(s) of the library

So knihovny is in the genitive singular, showing possession/association (door of the library).
If you said na dveřích v knihovně, that would mean on the door inside the library, a slightly different idea (location inside vs. belonging to).

Why is the verb je singular when dveřích looks plural?

The grammatical subject of the sentence is velký text (a big text), which is singular.
Na dveřích knihovny is just a prepositional phrase giving location.

So the structure is:

(Na dveřích knihovny) – on the door of the library (location)
je – is (3rd person singular)
velký text – a big text (subject)

The verb agrees with velký text, not with dveřích. This is exactly like English:
On the door of the library *is a big sign.*

Is velký text the natural way to say a big sign in Czech?

It is grammatically correct, but stylistically a bit unusual in everyday language.

text usually suggests a piece of writing as content: a text of an article, a message, the wording of a law, etc.
For a sign/writing on a door, the most natural word is nápis (inscription, lettering, sign).

More idiomatic would be:

Na dveřích knihovny je velký nápis Otevřeno od devíti do pěti.
There is a big sign “Open from nine to five” on the library door.

You can still use text, e.g. if you want to stress the written content rather than the physical sign, but nápis is what natives usually say here.

What exactly is Otevřeno grammatically, and why not otevřená?

Otevřeno comes from the verb otevřít (to open). Grammatically, it is a neuter short-form passive participle / verbal adjective used impersonally to express a state:

(Je) otevřeno. – It is open. (e.g. the shop is open.)

On signs you will often see just Otevřeno or Zavřeno, without je.

If you mention the library explicitly, you usually use the regular long-form adjective that agrees with knihovna (feminine):

Knihovna je otevřená od devíti do pěti. – The library is open from nine to five.

So:

Otevřeno od devíti do pěti – sign-style, impersonal
Knihovna je otevřená od devíti do pěti. – full sentence about the library

Why are the numbers devíti and pěti used instead of devět and pět?

Because of case and prepositions. The basic (nominative) forms are:

9 – devět
5 – pět

The genitive forms are:

9 – devíti
5 – pěti

The prepositions od (from, since) and do (to, until) require the genitive:

od devíti do pěti (hodin) – from nine to five (o’clock)
od pondělí do pátku – from Monday to Friday

So:

v devět – at nine (accusative, same form as nominative here)
od devíti – from nine (genitive → devíti)

How would you say from 9 a.m. to 5 p.m. more precisely on an actual sign in Czech?

Czech normally avoids a.m./p.m. and uses either context or the 24‑hour system. Typical sign-style options:

Otevřeno od 9 do 17 hodin.
Otevřeno 9–17
Otevřeno 9.00–17.00

Spelled out:

Otevřeno od devíti do sedmnácti hodin.

If you really want to use a 12‑hour feel in speech, you can say:

Otevřeno od devíti ráno do pěti odpoledne.

but on a real sign you’re much more likely to see 9–17 or 9.00–17.00.

Can you leave out velký text and just say that the door “says” Otevřeno od devíti do pěti?

Yes, that is very natural. Common variants include:

Na dveřích knihovny je napsáno: Otevřeno od devíti do pěti.
On the library door it is written: Open from nine to five.
Na dveřích knihovny je nápis: Otevřeno od devíti do pěti.

In everyday speech you might even just say:

Na dveřích mají Otevřeno od devíti do pěti.
On the door they have “Open from nine to five”.

So velký text is not required; you can replace it with nápis, je napsáno, or omit it when the meaning is clear.

Is the word order Na dveřích knihovny je velký text Otevřeno od devíti do pěti fixed?

No, Czech word order is quite flexible. Several versions are possible and grammatically correct; they just differ slightly in emphasis:

Na dveřích knihovny je velký text Otevřeno od devíti do pěti.
Neutral: first give the place (on the door), then say what is there.
Velký text Otevřeno od devíti do pěti je na dveřích knihovny.
Emphasis on what the text is, then you add where it is.
Na dveřích knihovny je nápis Otevřeno od devíti do pěti.
Same pattern with a more idiomatic noun.

If you start with Je:

Je na dveřích knihovny velký text Otevřeno od devíti do pěti?
This sounds like a yes/no question: Is there a big text “Open from nine to five” on the library door?

So the original order is a natural declarative, but not the only possible one.

What about the quotation marks around Otevřeno od devíti do pěti in Czech?

In Czech typography the standard quotation marks are:

opening: „
closing: “

So in printed Czech you will see something like:

Na dveřích knihovny je velký text „Otevřeno od devíti do pěti“.

In informal writing (email, SMS, online), many people just use straight English-style quotes ("Otevřeno od devíti do pěti").
On the actual door sign there would normally be no quotation marks at all – just:

Otevřeno od 9 do 17 hodin
or simply Otevřeno 9–17.