Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	Apr. 03, 2022	Oct. 03, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,326.1	$ 1,338.2
Accumulated amortization	(1,168.5)	(1,084.7)
Total estimated future amortization expense	157.6	253.5
Acquired and reacquired rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	1,126.7	1,141.5
Accumulated amortization	(1,040.5)	(971.9)
Total estimated future amortization expense	86.2	169.6
Acquired trade secrets and processes
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6	27.6
Accumulated amortization	(26.2)	(24.8)
Total estimated future amortization expense	1.4	2.8
Trade names, trademarks and patents
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	127.4	126.3
Accumulated amortization	(61.7)	(51.9)
Total estimated future amortization expense	65.7	74.4
Licensing agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	20.1	18.8
Accumulated amortization	(15.8)	(13.5)
Total estimated future amortization expense	4.3	5.3
Other finite-lived intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	24.3	24.0
Accumulated amortization	(24.3)	(22.6)
Total estimated future amortization expense	$ 0.0	$ 1.4