Goodwill and Intangible Assets (Schedule of Gross Intangibles) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021
Finite-lived Intangible Assets [Roll Forward]
Acquisitions	$ 1,991.0
Translation Adjustments	(20.9)
Total Gross Intangibles	$ 3,002.1	$ 1,032.0
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	16 years
Finite-lived Intangible Assets [Roll Forward]
Intangible assets, beginning of period	$ 708.6
Acquisitions	1,643.0
Translation Adjustments	(16.2)
Intangible assets, end of period	$ 2,335.4
Technology
Finite-Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	13 years
Finite-lived Intangible Assets [Roll Forward]
Intangible assets, beginning of period	$ 146.3
Acquisitions	105.0
Translation Adjustments	(1.2)
Intangible assets, end of period	$ 250.1
Trademarks
Finite-Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	10 years
Finite-lived Intangible Assets [Roll Forward]
Intangible assets, beginning of period	$ 160.5
Acquisitions	243.0
Translation Adjustments	(3.5)
Intangible assets, end of period	$ 400.0
Patent and Engineering Drawings
Finite-Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	5 years
Finite-lived Intangible Assets [Roll Forward]
Intangible assets, beginning of period	$ 16.6
Acquisitions	0.0
Translation Adjustments	0.0
Intangible assets, end of period	$ 16.6