Income Taxes - Deferred Income Tax (Details) - USD ($) $ in Millions	Jan. 01, 2023	Jan. 02, 2022
Long-term:
Accrued liabilities	$ 32.0	$ 52.6
Inventory valuation	30.3	41.5
Accrued vacation	8.3	9.6
Deferred compensation and other benefit plans	12.7	39.1
Postretirement benefits other than pensions	1.0	1.7
Operating lease liabilities	29.9	38.7
Capitalization of research and development	70.8	34.1
Tax credit and net operating loss carryforward	44.6	47.4
Other	32.6	0.0
Valuation allowance	(16.1)	(12.7)
Total deferred income tax assets	246.1	252.0
Long-term:
Intangible amortization	646.9	751.5
Property, plant and equipment differences	31.9	37.8
Operating lease right-of-use assets	26.7	35.0
Unremitted earnings of foreign subsidiaries	3.1	15.9
Other	12.9	7.9
Total deferred income tax liabilities	721.5	848.1
Net deferred income tax liabilities	$ 475.4	$ 596.1

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Amount of deferred tax liability attributable to taxable temporary differences.

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Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences, classified as other.

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Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from postretirement benefits.

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Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

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Amount of deferred tax liability attributable to taxable temporary differences from property, plant, and equipment.

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Amount of deferred tax liability attributable to taxable temporary differences from undistributed earnings of subsidiary and other recognized entity not within country of domicile. Includes, but is not limited to, other basis differences.

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