Business Combinations, Goodwill and Acquired Intangible Assets - Acquired Intangible Assets (Details) - USD ($) $ in Millions	Oct. 02, 2022	Jan. 02, 2022
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 2,209.9	$ 2,406.2
Accumulated amortization	630.2	521.7
Net carrying amount	1,579.7	1,884.5
Total acquired intangible assets, gross carrying amount	3,052.0	3,263.3
Acquired intangible assets, net	2,421.8	2,741.6
Trademarks
Acquired Finite-Lived Intangible Assets [Line Items]
Intangible assets not subject to amortization, gross carrying amount	842.1	857.1
Proprietary technology
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,610.4	1,767.7
Accumulated amortization	445.8	358.2
Net carrying amount	1,164.6	1,409.5
Customer list/relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	577.2	616.2
Accumulated amortization	163.3	141.8
Net carrying amount	413.9	474.4
Patents
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	0.6	0.6
Accumulated amortization	0.6	0.6
Net carrying amount	0.0	0.0
Non-compete agreements
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	0.9	0.9
Accumulated amortization	0.9	0.9
Net carrying amount	0.0	0.0
Trademarks
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	5.4	4.5
Accumulated amortization	4.2	3.9
Net carrying amount	1.2	0.6
Backlog
Acquired Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	15.4	16.3
Accumulated amortization	15.4	16.3
Net carrying amount	$ 0.0	$ 0.0