Augustus the Architect has dog at home (5)

I believe the answer is:

pugin

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'augustus the architect' is the definition.
I can't tell whether this definition defines the answer.

'dog at home' is the wordplay.
'dog' becomes 'pug' (pug is a kind of dog).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'pug'+'in'='PUGIN'

'has' acts as a link.

Can you help me to learn more?

(Other definitions for pugin that I've seen before include "Architect" , "One-time designer" , "Augustus -, Palace of Westminster designer" , "one known for his work inside and outside Parliament" .)

I've seen this clue in The Times.

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