Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	Jan. 02, 2022	Oct. 03, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,338.0	$ 1,338.2
Accumulated amortization	(1,132.3)	(1,084.7)
Total estimated future amortization expense	205.7	253.5
Acquired and reacquired rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,138.1	1,141.5
Accumulated amortization	(1,009.5)	(971.9)
Total estimated future amortization expense	128.6	169.6
Acquired trade secrets and processes
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6	27.6
Accumulated amortization	(25.4)	(24.8)
Total estimated future amortization expense	2.2	2.8
Trade names, trademarks and patents
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	126.9	126.3
Accumulated amortization	(56.8)	(51.9)
Total estimated future amortization expense	70.1	74.4
Licensing agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	21.2	18.8
Accumulated amortization	(16.4)	(13.5)
Total estimated future amortization expense	4.8	5.3
Other finite-lived intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	24.2	24.0
Accumulated amortization	(24.2)	(22.6)
Total estimated future amortization expense	$ 0.0	$ 1.4