Database Connections is in the left directory tree in Arccatalog.
After double-clicking, select Database Plantform:postgresql, instance for localhost (127.0.0.1), enter the user and password (default user postgres), database is best not to select the default system database Postgres (some will be prompted not to select the system database)
Unable to connect to database server to retrieve database list; Please verify your server name, user name and password info and try again.
Or
Cannot connect to database because client software failed to load. Be sure the database client software is installed and configured correctly.
1. Please check the connection client configuration.
http://support.esri.com/en/technical-article/000011608
Http://resources.arcgis.com/en/help/main/10.1/index.html#/Setting_up_a_connection_to_PostgreSQL/002p0000003q000000/
Download the DLL configuration file into the ArcGIS Bin directory.
If not, see 2.
2, which may be the result of PostgreSQL or PostGIS version digits mismatch with the number of ArcGIS digits
Https://my.oschina.net/jasonzhang/blog/655731?p={{totalpage}}
https://www.zhihu.com/question/28976663
Arccatalog/arcgis How to connect Postgresql/postpis