The definitions of regional formations (name, type location, characteristic lithology, age constraints) have been compiled for different regions.  These “stratigraphic unit databases” or “stratigraphic lexicons” are generally searchable.

International Geology Website and Database (supported by the Geologic TimeScale Foundation and Deep Time Digital Earth (DDE))
      https://geolex.org/   
This website gives access to the following individual Country formation lexicons.
China  https://chinalex.geolex.org
India   http://indplex.geolex.org
Vietnam   https://vietlex.geolex.org
Niger   https://nigerlex.geolex.org
Nigeria  https://nigerialex.geolex.org
Thailand  https://thailex.geolex.org
Panama   https://panamalex.geolex.org
Africa   https://africalex.geolex.org
Qatar   https://qatarlex.geolex.org
Middle East  https://mideastlex.geolex.org

Lithostratigraphic Units of North-West Europe -- formerly "NORLEX"
      Click here to enter the site     

Australia -- Geoscience Australia “Stratigraphic Units Database”
            http://www.ga.gov.au/data-pubs/datastandards/stratigraphic-units
Search the database (http://dbforms.ga.gov.au/www/geodx.strat_units.int) by name, region, etc.  In addition to a summary of lithology (for most) and references, the returned page for each formation or member also includes navigation links to overlying/underling units.

New Zealand – GNS Science “New Zealand Stratigraphic Lexicon”
            http://data.gns.cri.nz/stratlex/
Search the database by name, region, age, etc.  The returned page for each formation or member provides references, but without a lithology summary.

British Isles – British Geologic Survey “BGS Lexicon of Named Rock Units”
Search (http://www.bgs.ac.uk/lexicon/home.cfm) on rock name and age.  The returned page includes lithologic description, contacts, extent, type locality and references. 

United States – U.S. Geologic Survey “GEOLEX; National Geologic Map Database, Geologic Names Lexicon”
            http://ngmdb.usgs.gov/Geolex/geolex_home.html
Search the database by name, region, age, citation, etc.  The returned page for each formation or member provides references, but without a lithology summary.
The returned page gives age, type location and history; and the lithology summary is hidden under the “History” link.

Canada -- National Geological Surveys Committee, Canadian Geoscience Knowledge Network “WEBLEX Canada -- Lexicon of Canadian Geologic Names on-line”
            https://weblex.nrcan.gc.ca/weblexnet4/weblex_e.aspx
Search by name, region, age and/or author.  The returned page has lithology and age summaries, type location, extent and  references.

Austria – LithStrat
            http://resource.geolba.ac.at/GeologicUnit.html

Switzerland – Stratigraphic Lexicon
            Introduction: https://www.geologieportal.ch/en/knowledge/lookup/stratigraphic-lexicon.html
Search the database: https://www.strati.ch/swisstopo.strati/frontend/index?language=en"