Linking first and second level composite primary keys I am trying to create a new database with a hierarchical structure of two many-to-many tables using composite keys. Unfortunately the creation of tables fails stating that the foreign keys do not match:

Here a simplified Structure of the sql query:

CREATE TABLE a(
    a_ID serial PRIMARY KEY,
    a_name char(100)
);

CREATE TABLE b(
    b_ID serial PRIMARY KEY,
    b_name char(100)
);

CREATE TABLE c(
    c_ID serial PRIMARY KEY,
    c_name char(250),
);

-- First refering table
CREATE TABLE b_c(
    b_ID INT references b ON UPDATE CASCADE,
    c_ID INT references c ON UPDATE CASCADE,
    PRIMARY KEY (b_ID, c_ID)
);
-- Second higher level combining 
CREATE TABLE full(
    b_c_ID INT references b_c ON UPDATE CASCADE,
    a_ID INT references a ON UPDATE CASCADE,
    PRIMARY KEY (b_c_ID, a_ID)
);


The creation of the last table fails. 
Am I missing something here or is it impossible to refer to a composite primary key in just another composition?
Any comments?
You need 2 columns in the foreign key constraint, to refer to a table with  2 columns in the primary key:

-- Second higher level combining 
CREATE TABLE full_b_c(
    b_ID INT NOT NULL,
    c_ID INT NOT NULL,
    a_ID INT NOT NULL references a ON UPDATE CASCADE,
    PRIMARY KEY (b_ID, c_ID, a_ID),
    FOREIGN KEY (b_ID, c_ID) 
      references b_c (b_ID, c_ID) ON UPDATE CASCADE
);