Business Acquisitions, Goodwill and Acquired Intangible Assets (Other Acquired Intangible Assets) (Details) - USD ($) $ in Millions	Jan. 02, 2022	Jan. 03, 2021
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	$ 2,406.2	$ 611.2
Accumulated amortization	521.7	377.2
Net carrying amount	1,884.5	234.0
Total acquired intangible assets, gross carrying amount	3,263.3	786.9
Acquired intangible assets, net	2,741.6	409.7
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Trademarks	857.1	175.7
Proprietary technology
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	1,767.7	420.3
Accumulated amortization	358.2	242.7
Net carrying amount	1,409.5	177.6
Customer list/relationships
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	616.2	168.3
Accumulated amortization	141.8	112.8
Net carrying amount	474.4	55.5
Patents
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	0.6	0.7
Accumulated amortization	0.6	0.7
Net carrying amount	0.0	0.0
Non-compete agreements
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	0.9	0.9
Accumulated amortization	0.9	0.9
Net carrying amount	0.0	0.0
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	4.5	4.5
Accumulated amortization	3.9	3.6
Net carrying amount	0.6	0.9
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	16.3	16.5
Accumulated amortization	16.3	16.5
Net carrying amount	$ 0.0	$ 0.0