Post-employment benefits - Assumptions used for defined benefit obligations in Germany, the United States and the rest of the world (Detail)	Dec. 31, 2022	Dec. 31, 2021
Post-employment benefits [Line Items]
Actuarial assumption of discount rates	4.70%	1.80%
Actuarial assumption of expected rates of inflation	2.20%	2.00%
Actuarial assumption of expected rates of salary increases	2.90%	2.60%
Germany [Member]
Post-employment benefits [Line Items]
Actuarial assumption of discount rates	4.10%	1.10%
Actuarial assumption of expected rates of inflation	2.00%	1.80%
Actuarial assumption of expected rates of salary increases	2.80%	2.50%
United States of America [Member]
Post-employment benefits [Line Items]
Actuarial assumption of discount rates	5.20%	2.60%
Actuarial assumption of expected rates of inflation	2.30%	2.20%
Actuarial assumption of expected rates of salary increases	0.00%	0.00%
Other countries [Member]
Post-employment benefits [Line Items]
Actuarial assumption of discount rates	4.90%	2.10%
Actuarial assumption of expected rates of inflation	2.60%	2.00%
Actuarial assumption of expected rates of salary increases	3.30%	2.90%