1) Create tablespace for example name catalog_tbs
2) Create user for example user rman_catalog and assign catalog_tbs as default tablespace
3) Grant user rman_catalog the following roles: connect, resource, recovery_catalog_owner.
4) Connect to catalog through RMAN
5) Create recovery catalog
$ rman catalog=rman_catalog/password

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connected to recovery catalog database

RMAN> create catalog tablespace catalog_tbs;

recovery catalog created

6) Next register database with the catalog
$ rman target=sys/syspassword catalog=rman_catlog/password

RMAN> register database;

database registered in recovery catalog
starting full resync of recovery catalog
full resync complete

Note: One can register multiple databases with different versions in the same catalog but the catalog version is the highest version of the databases registered so if you upgrade a database the catalog will need to be upgraded.

To upgrade the catalog, it is included in the steps of upgrade how to upgrade the catalog, below shows how to upgrade the catalog.

RMAN> upgrade catalog;

recovery catalog owner is RMAN_CAT
enter UPGRADE CATALOG command again to confirm catalog upgrade

RMAN> upgrade catalog;

recovery catalog upgraded to version 10.02.00.00
DBMS_RCVMAN package upgraded to version 10.02.00.00
DBMS_RCVCAT package upgraded to version 10.02.00.00