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"Cat"  in "equal to a cat" serves as a part of the subject complement.  COMPLEMENT means "a word or phrase that follows a verb and describes the subject of the verb. In ‘John is cold’ and ‘John became chairman’, ‘cold’ and ‘chairman’ are complements. ( From Longman Dictionary)   In the pattern, "subject + copula + adjective + preposition + NOUN, the combination after  the copula is the subject complement.  In "I'm a cat.,"  "a cat" is the subject complement.

To add to f6pafd's correct answer, "a cat" is object to the preposition "to" within the phrase "to a cat" that complementizes the head of the subject complement "equal" in the sentence A dog is equal to a cat. "A cat" would be part of the subject if placed before the verb:

- A dog and a cat are equal.

And it would be an object if placed after a transitive verb.

- A dog chases a cat.

When a copulative verb such as be is used, the subject and the subject complement are identified with the same referent (I = a cat), but syntactically speaking only what comes before the verb is the subject—what follows is, as f6pafd said, the subject complement.

Last edited by Gustavo, Co-Moderator

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