Why "Ihre" and not "Ihrer"?

Question

Why "Ihre" and not the genitive "Ihrer" in the following sentence? I thought that we have to use the genitive case to show possession?

Ihre Katze war krank.

Answer 1

Using the genitive is one method to express possession:

Barbaras Katze war krank.

Die Katze des Königs war krank.

However, we also have possessive pronouns to do the same job, and these don't trigger the genitive. Instead, they conform to the case of the word that they accompany.

"Ihre" expresses that the possessor is female and singular, while the possessed object is feminine, singular, and in the nominative.

Answer 2

How do nominal phrases work?

The part »ihre Katze« (her cat) is the subject of the sentence, and the subject (the whole thing) must always be in nominative case.

The subject is very often a nominal phrase or noun phrase which means, that is consists of two or more words, and that it has a noun as its core (or head), which is Katze (cat) in your sentence. Nominal phrases can be much longer than just two words. The sequence of bold marked words in the next example is one nominal phrase, and it is the subject of the sentence.

Das häufige und völlig unnötige Nennen ihres zweiten Vornamens verärgerte ihn.
_{The frequent and completely unnecessary mention of her middle name annoyed him.}

The other parts that are inside a nominal phrase can be determiners and attributes. The core of this example is the noun Nennen (mention). It has an article (das = the) as determiner and a list of adjectives (häufige und völlig unnötige = frequent and completely unnecessary) as left attribute and another nominal phrase in genitive case (ihres zweiten Vornamens = of her middle name) as a right attribute.

Note, that the whole nominal phrase (all 9 words) are the subject of the sentence, and that the complete nominal phrase, as a whole and undivided thing, is in nominative case. But parts of this phrase still can be in other grammatical cases. The nominal phrase works like a container. The container is in nominal case and it is used as a sentence's subject. And this outside behavior is independent from its inner anatomy.

Btw: The very same nominal phrase can also be used as an object in some other grammatical case in another sentence, as shown here:

Walter vermeidet das häufige und völlig unnötige Nennen ihres zweiten Vornamens.
Walter avoids the frequent and completely unnecessary mention of her middle name.

The verb vermeiden (to avoid) needs its object to be in accusative case, and so the whole nominal phrase is in accusative case (it is an accusative object here). But still it contains parts in other cases ("ihres zweiten Vornamens" is still in genitive case).

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How to determine possession?

1. possessive attributes

1.1 genitive attributes

One way to express possession is the usage of nominal phrases in genitive case that are attached to the core of another nominal group. They come as left attribute and as right attribute.

1.1.1 left genitive attribute

Deutschlands Bundeskanzler nimmt an dem Treffen der G7-Staaten teil.
^{Germany's chancellor attends the meeting of the G7 countries.}

»Deutschlands Bundeskanzler« is a nominal group in nominative case (it is the subject of the sentence). The core of this group is Bundeskanzler which is in the same case as the whole nominal group, and it has a left possessive attribute in genitive case (Deutschlands = Germany's) which is a nominal group that consists of only a core without any additional parts.

1.1.2 right genitive attribute

Deutschlands Bundeskanzler nimmt an dem Treffen der G7-Staaten teil.
^{Germany's chancellor attends the meeting of the G7 countries.}

The nominal phrase dem Treffen der G7-Staaten is in dative case, it is the dative object of this sentence. It's core is the noun Treffen (meeting), and this core has an article as determiner (dem = the) and a right possessive attribute in genitive case (der G7-Staaten = of the G7 countries) which has the noun G7-Staaten as its core and an article as determiner (der = the).

1.2 von-attributes

Der Bundeskanzler von Deutschland nimmt an dem Treffen der G7-Staaten teil.
^{The chancellor of Germany attends the meeting of the G7 countries.}

Very often you can use a von-construction instead of a constriction in genitive case, which is "of" in English. Note that although this is a possessive construct, no genitv is used here.

2. possessive pronouns

Pronouns are used to refer to something that otherwise would be described using a nominal phrase.

Deutschland ist ein großes Land in Europa. Sein Bundeskanzler nimmt an dem Treffen der G7-Staaten teil.
^{Germany is a big country in Europe. Its chancellor is attending the meeting of the G7 countries.}

The left genitive attribute from 1.1.1 is here replaced by a possessive pronoun. It refers to a nominal phrase (here just one noun) in the preceding sentence.

This possessive pronoun is a completely different construction than a possessive attribute, so there is no reason why it should be in genitive case too. Instead it matches the case of the core of the nominal group.

Answer 3

Even in english, it's "Her cat was sick", not "Hers cat was sick". "Her" is in the nominative case, it would be wrong to use it in genitive.

Answer 4

Pronoun cannot be used in the prefixed possessive function of the Genitiv, only for proper Genitivobjekte (which are rare in German and on the decline) or suffixed possessive constructs. "Barbaras Katze war krank" is fine, "Ihrer Katze war krank" is wrong, "Die Katze Barbaras war krank" is a bit archaic, "Die Katze ihrer war krank" is not exactly wrong but utterly archaic and without a use case one would not rather express in a different manner. "Die Katze gedachte ihrer" is fine (though probably weird to say of a cat) and one of the few constructs that will quite refuse to work with anything but a Genitivobjekt.

Answer 5

"Ihre" is the genitive (indicating possession) of a grammatically female object. The genitive for a grammatically male object would be

Mein, dein, sein, ihr, sein, unser, euer, ihr. 

Since the cat is gramatically female in German, it is

Meine Katze, deine Katze, seine Katze, ihre Katze, seine Katze, unsere Katze, eure Katze, ihre Katze. 

Since the owner is singular, grammatically female, it is "Ihre Katze".

"Ihrer Katze" would be dative. For example, "Barbara zeigte ihrer Katze ein Bild einer Maus".