SUPPLEMENTAL EQUITY AND COMPREHENSIVE INCOME INFORMATION - Reclassification Adjustment Out of Accumulated Other Comprehensive loss (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Amounts reclassified from Accumulated other comprehensive loss
Cost of products sold	$ (6,095.5)	$ (5,048.2)	$ (5,166.0)
Income before taxes	992.6	737.3	249.5
Provision for (benefit from) income taxes	(248.6)	(177.7)	56.7
Net income (loss)	740.1	555.9	303.6
Income tax (benefit) expense allocated - Foreign currency translation:
Translation gain (loss)	(23.2)	27.5	(5.5)
Income tax (benefit) expense allocated - Pension and other postretirement benefits:
Net gain recognized from actuarial gain/loss and prior service cost/credit	8.5	3.1	19.4
Reclassifications to net income	1.6	0.9	179.3
Income tax (benefit) expense allocated - Cash flow hedges:
Gains (losses) recognized on cash flow hedges	1.7	(2.3)	0.2
Reclassifications to net income	(0.5)		(0.5)
Income tax (benefit) expense allocated to components of other comprehensive income (loss)	(11.9)	29.2	192.9
Amounts Reclassified from Accumulated other comprehensive loss
Amounts reclassified from Accumulated other comprehensive loss
Net income (loss)	(2.7)	(2.8)	(264.7)
Pension and Other Postretirement Benefits | Amounts Reclassified from Accumulated other comprehensive loss
Amounts reclassified from Accumulated other comprehensive loss
Other non-operating expense (income), net	(6.0)	(3.8)	(445.4)
Provision for (benefit from) income taxes	1.6	0.9	179.3
Net income (loss)	(4.4)	(2.9)	(266.1)
Cash Flow Hedges | Amounts Reclassified from Accumulated other comprehensive loss
Amounts reclassified from Accumulated other comprehensive loss
Income before taxes	2.2	0.1	1.9
Provision for (benefit from) income taxes	(0.5)		(0.5)
Net income (loss)	1.7	0.1	1.4
Cash Flow Hedges | Amounts Reclassified from Accumulated other comprehensive loss | Foreign exchange contracts
Amounts reclassified from Accumulated other comprehensive loss
Cost of products sold	1.3	0.7	2.1
Cash Flow Hedges | Amounts Reclassified from Accumulated other comprehensive loss | Commodity contracts
Amounts reclassified from Accumulated other comprehensive loss
Cost of products sold	$ 0.9	$ (0.6)	$ (0.2)