Detectives believe a man found dead near a waste chute at an apartment complex was assaulted.
It is believed the victim discovered at City Garden apartments at Northgate Street in Cork was Irish and aged in his 60s.
He may have been homeless at the time of his killing.
A post-mortem examination was carried out by deputy state pathologist Margaret Bolster but gardai said they were not releasing the details for "operational reasons".
However they confirmed the man was subject to an assault before his death.
Gardai were called to the scene at around 5.30pm on Monday evening. The victim's body was discovered close to a waste chute running from the top to the bottom of the five-storey complex.
It is understood investigators believe they may know the identity of the man but have yet to confirm it.
"Although progress has been made in relation to the identification of the male gardai are not in a position to formally identify him and wish to seek the assistance of the public," a Garda spokesman said.
The man is described as being of slight build, approximately 5ft 5in to 5ft 6in, and with white/grey hair and moustache. He was wearing a beige fleece top, black T-shirt and beige trousers.
Detectives have also appealed to anyone who may have seen a man fitting this description in the North Main Street/Bachelors Quay or City Garden apartment areas between last Saturday and last night to get in contact.