Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	Jul. 03, 2022	Oct. 03, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,251.1	$ 1,338.2
Accumulated amortization	(1,144.8)	(1,084.7)
Total estimated future amortization expense	106.3	253.5
Acquired and reacquired rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,054.3	1,141.5
Accumulated amortization	(1,013.5)	(971.9)
Total estimated future amortization expense	40.8	169.6
Acquired trade secrets and processes
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6	27.6
Accumulated amortization	(26.8)	(24.8)
Total estimated future amortization expense	0.8	2.8
Trade names, trademarks and patents
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	128.0	126.3
Accumulated amortization	(66.8)	(51.9)
Total estimated future amortization expense	61.2	74.4
Licensing agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	18.0	18.8
Accumulated amortization	(14.5)	(13.5)
Total estimated future amortization expense	3.5	5.3
Other finite-lived intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	23.2	24.0
Accumulated amortization	(23.2)	(22.6)
Total estimated future amortization expense	$ 0.0	$ 1.4