apologies >> /əˈpɒlədʒi/
Definition: [noun] A regretful acknowledgement of an offence or failure.
Example: we owe you an apology
Definition: [noun] A very poor or inadequate example of.
Example: we were shown into an apology for a bedroom
Definition: [noun] another term for apologia
Example: We can write letters to foreign newspapers, websites, post personal apologies on our blogs.