Greet mother on time by the front door (7,3)

'the front door' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
I also know that 'front door' relates to this answer.

'greet mother on time' is the wordplay.
'greet' becomes 'welcome' (welcoming is a kind of greeting).
'mother' becomes 'ma' (ma can mean mother).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'time' becomes 't' (abbreviation).
'welcome'+'ma'+'t'='WELCOME MAT'

'by' is the link.

Can you help me to learn more?