Goodwill and other intangible assets - intangible assets (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Finite-lived intangible assets
Gross value	$ 5,791.7	$ 6,520.8
Accumulated amortization	1,750.7	1,472.8
Carrying value	4,041.0	5,048.0
Indefinite-lived	92.3	92.3
Total	4,133.3	5,140.3
Amortization	318.3	290.8	$ 307.5
Customer relationships
Finite-lived intangible assets
Gross value	4,806.4	5,474.2
Accumulated amortization	1,333.5	1,121.6
Carrying value	3,472.9	4,352.6
Trade names
Finite-lived intangible assets
Gross value	354.4	505.1
Accumulated amortization	205.1	194.1
Carrying value	149.3	311.0
Other
Finite-lived intangible assets
Gross value	630.9	541.5
Accumulated amortization	212.1	157.1
Carrying value	$ 418.8	$ 384.4

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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