Business Acquisitions, Goodwill and Acquired Intangible Assets (Provisional Fair Values Allocated to Assets Acquired and Liabilities Assumed) (Details) - USD ($) $ in Millions		12 Months Ended
	May 14, 2021	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Business Acquisition [Line Items]
Goodwill		$ 7,986.7	$ 2,150.0	$ 2,050.5
Acquired intangible assets			7.0
Acquisitions and other investments, net of cash acquired			$ 29.0
FLIR
Business Acquisition [Line Items]
Cash and cash equivalents		287.7
Accounts receivable, net		241.3
Unbilled receivables, net		72.2
Inventories, net		531.8
Prepaid expenses and other current assets		55.2
Total current assets		1,188.2
Property, plant and equipment		356.3
Goodwill		5,905.5
Acquired intangible assets	$ 2,490.0	2,490.0
Other long-term assets		151.5
Total assets acquired		10,091.5
Accounts payable		144.8
Accrued liabilities		629.5
Total current liabilities acquired		774.3
Long-term debt, net		496.8
Long-term deferred tax liabilities		646.5
Other long-term liabilities		265.3
Total liabilities assumed		2,182.9
Consideration transferred		7,908.6
Acquisitions and other investments, net of cash acquired	7,620.9	$ 7,620.9
Net share issuances	$ 3,900.0