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Multi-Column Primary Key in MySQL 5

I'm trying to learn how to use keys and to break the habit of necessarily having SERIAL type IDs for all rows in all my tables. At the same time, I'm also doing many-to-many relationships, and so requiring unique values on either column of the tables that coordinate the relationships would hamper that.

How can I define a primary key on a table such that any given value can be repeated in any column, so long as the combination of values across all columns is never repeated exactly?

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Quoted from the CREATE TABLE Syntax page:

A PRIMARY KEY can be a multiple-column index. However, you cannot create a multiple-column index using the PRIMARY KEY key attribute in a column specification. Doing so only marks that single column as primary. You must use a separate PRIMARY KEY(index_col_name, ...) clause.

Something like this can be used for multi-column primary keys:

CREATE TABLE
    product (
        category INT NOT NULL,
        id INT NOT NULL,
        price DECIMAL,
        PRIMARY KEY(category, id)
    );

From 13.1.20.6 FOREIGN KEY Constraints


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