Segments and geographic information - Management EBITDA by segment (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022		Jan. 03, 2021		Dec. 29, 2019
Segment Reporting Information [Line Items]
Depreciation and amortization	$ (328.1)		$ (325.9)		$ (327.5)
Interest expense, net	(146.0)		(198.2)		(231.4)
Stock-based compensation	(22.5)		(8.6)		(18.6)
Restructuring and severance-related costs	(8.2)		(11.7)		(36.0)
Tax indemnification expense, net	(0.8)		(31.2)		(29.2)
EU medical device regulation transition costs	(4.0)		(4.3)		(3.2)
Unrealized foreign currency exchanges losses, net			(63.0)		19.6
Other adjustments	(9.5)		(10.5)		(35.2)
Management adjustments and realized foreign exchange losses					(21.9)
Loss before provision for (benefit from) income taxes	(26.0)		(225.3)		(180.8)
Operating Segments
Segment Reporting Information [Line Items]
Management EBITDA					680.5
Operating Segments | Americas
Segment Reporting Information [Line Items]
Management EBITDA					418.4
Operating Segments | EMEA
Segment Reporting Information [Line Items]
Management EBITDA					54.9
Operating Segments | Greater China
Segment Reporting Information [Line Items]
Management EBITDA					118.4
Operating Segments | Other
Segment Reporting Information [Line Items]
Management EBITDA					88.8
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Corporate	$ (241.5)	[1]	$ (230.4)	[1]	$ (177.9)	[2]

[1] Corporate primarily consists of costs related to executive and staff functions, including certain finance, human resources, manufacturing, and information technology, which benefit the enterprise as a whole. These costs are primarily related to the general management of these functions on a corporate level and the design and development of programs, policies, and procedures that are then implemented in the individual segments, with each segment bearing its own cost of implementation. The Company’s Corporate function also includes debt and stock-based employee compensation expense associated with all employee stock-based awards.

[2] Corporate primarily consists of costs related to executive and staff functions, including certain finance, human resources, manufacturing, and information technology, which benefit the enterprise as a whole. These costs are primarily related to the general management of these functions on a corporate level and the design and development of programs, policies, and procedures that are then implemented in the individual segments, with each segment bearing its own cost of implementation. The Company’s Corporate function also includes debt and stock-based employee compensation expense associated with all employee stock-based awards.