Goodwill and Other Intangible Assets - Summary of Gross Carrying Amount and Accumulated Amortization of Intangible Assets (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021
Finite Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,953.6	$ 1,963.7
Accumulated amortization	(1,074.4)	(947.0)
Net book value	$ 879.2	1,016.7
Estimated useful lives	5 years
Technology
Finite Lived Intangible Assets [Line Items]
Gross carrying amount	$ 968.3	970.3
Accumulated amortization	(460.2)	(395.1)
Net book value	$ 508.1	$ 575.2
Technology | Minimum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	10 years	10 years
Technology | Maximum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	15 years	15 years
Customer Relationships
Finite Lived Intangible Assets [Line Items]
Gross carrying amount	$ 610.3	$ 618.3
Accumulated amortization	(381.5)	(333.8)
Net book value	$ 228.8	$ 284.5
Customer Relationships | Minimum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	5 years	5 years
Customer Relationships | Maximum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	12 years	12 years
Corporate Tradename
Finite Lived Intangible Assets [Line Items]
Gross carrying amount	$ 164.4	$ 164.8
Accumulated amortization	(61.7)	(53.5)
Net book value	$ 102.7	$ 111.3
Estimated useful lives	20 years	20 years
Other (Including Milestone Payments)
Finite Lived Intangible Assets [Line Items]
Gross carrying amount	$ 210.6	$ 210.3
Accumulated amortization	(171.0)	(164.6)
Net book value	$ 39.6	$ 45.7
Other (Including Milestone Payments) | Minimum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	4 years	4 years
Other (Including Milestone Payments) | Maximum
Finite Lived Intangible Assets [Line Items]
Estimated useful lives	14 years	14 years