Intangible assets - Finite-Lived and Indefinite-Lived Intangible Assets (Details) - USD ($) $ in Millions	Jul. 02, 2022	Jan. 01, 2022
Finite-Lived Intangible Assets
Finite-lived, cost	$ 2,157.8	$ 2,220.4
Finite-lived, accumulated amortization	(1,081.8)	(1,047.6)
Finite-lived, net	1,076.0	1,172.8
Indefinite-lived, cost	513.4	513.4
Indefinite-lived, accumulated impairment	(44.0)	(44.0)
Indefinite-lived, net	469.4	469.4
Cost	2,671.2	2,733.8
Accumulated amortization and impairment	(1,125.8)	(1,091.6)
Net	1,545.4	1,642.2
—Customer relationships
Finite-Lived Intangible Assets
Finite-lived, cost	1,967.9	2,031.7
Finite-lived, accumulated amortization	(931.3)	(901.6)
Finite-lived, net	1,036.6	1,130.1
—Technology
Finite-Lived Intangible Assets
Finite-lived, cost	90.4	90.9
Finite-lived, accumulated amortization	(89.3)	(89.4)
Finite-lived, net	1.1	1.5
—Capitalized software
Finite-Lived Intangible Assets
Finite-lived, cost	99.5	97.8
Finite-lived, accumulated amortization	(61.2)	(56.6)
Finite-lived, net	$ 38.3	$ 41.2