It is believed the fatal attack was a random one carried out by a man unknown to Ashling Murphy.
A man in his 40s is still being detained in connection with the murder of a young woman in Tullamore, Offaly on Wednesday.
The woman, who was in her early 20s, has been named locally as Ashling Murphy.
Murphy was well known in the area as she worked as a primary school teacher and was also involved in the arts.
She had been jogging on the banks of the Grand Canal at the time of the assault.
A murder investigation is underway and a post mortem examination will be carried out.
It is understood that another woman arrived on the scene during the fatal attack and disturbed the killer.
The man who was arrested is said to live in the Tullamore area but is not originally from the area.
With there being no link between the attacker and the victim, Gardaí are considering that the attack may have been random.
Minister for Justice Helen McEntee said her thoughts were with the family of the woman "killed in a truly shocking crime".
https://twitter.com/HMcEntee/status/1481384680477835266?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1481384680477835266%7Ctwgr%5E%7Ctwcon%5Es1_&ref_url=https%3A%2F%2Fwww.irishexaminer.com%2Fnews%2Farid-40783980.html
"Please anyone with information, come forward to An Garda Síochána," she continued.
"The Gardaí will investigate this awful crime and ensure justice is done".
Anyone with information is asked to contact Tullamore Garda Station on 057 932 7600, the Garda Confidential Line on 1800 666 111, or any Garda Station.
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