Business Acquisitions, Goodwill and Acquired Intangible Assets (Purchase Price) (Details) - USD ($) $ in Millions				12 Months Ended
	May 14, 2021	Jan. 05, 2020	Aug. 30, 2019	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Business Acquisition [Line Items]
Consideration transferred, net of cash acquired					$ 29.0
Goodwill Acquired				$ 5,905.5	16.9
Acquired intangible assets					7.0
Cash paid				3,723.3	29.0	$ 484.0
FLIR
Business Acquisition [Line Items]
Consideration transferred, net of cash acquired	$ 7,620.9			7,620.9
Goodwill Acquired	5,905.5
Acquired intangible assets	2,490.0			$ 2,490.0
Net share issuances	$ 3,900.0
OakGate Technology, Inc.
Business Acquisition [Line Items]
Goodwill Acquired					16.9
Acquired intangible assets					7.0
Cash paid		$ 28.5			28.5
Purchase price adjustment - Micralyne Inc. (acquired in 2019)
Business Acquisition [Line Items]
Goodwill Acquired					0.0
Acquired intangible assets					0.0
Cash paid			$ 25.7
Purchase price adjustment - Micralyne Inc. (acquired in 2019)					$ 0.5