In addition to issuing emoney, Square is authorised to provide payment services number 3b (execution of payment transactions through a payment card or a similar device) and number 5 (issuing of payment instruments and/or acquiring of payment transactions).
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Those firms in the above map which are indigenous to Ireland also appear on our bigger Fintech Ireland Map version 3.0 which you can find here.
If you are looking to get authorised in Ireland as an emoney or payments firm, see these Authorisation Guides.