Learn Hardcore Norwegian: Katten har skarpe klør.

Katt is the basic dictionary form, but Norwegian usually needs a full noun phrase in a sentence. Katten is the definite singular form, made by adding -en to katt. So:

en katt = indefinite singular
katten = definite singular

That means the noun itself carries the idea of the.

Why is there no separate word for the before katten?

In Norwegian, definiteness is often shown by an ending on the noun rather than by a separate word. So English the cat becomes katten.

A separate definite word like den is usually added when there is an adjective before the noun:

katten = the cat
den svarte katten = the black cat

So in your sentence, katten already means the cat by itself.

Why is the verb har the same form? Shouldn’t it change depending on the subject?

No. In modern Norwegian, verbs do not change for person or number in the present tense. So you get:

jeg har = I have
du har = you have
han har = he has
vi har = we have

So har works for all subjects. This is simpler than English, where you have have but also has.