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Share-based compensation - Narratives (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Dec. 29, 2018
Share-based Compensation Arrangement by Share-based Payment Award        
Share based compensation expense recognized   $ 24.6 $ 19.8 $ 15.0
Proceeds from stock options exercised $ 4.6 3.1 1.8  
—Share options        
Share-based Compensation Arrangement by Share-based Payment Award        
Aggregate intrinsic value of options that were vested or expected to vest $ 34.8      
Contractual term of options that were vested or expect to vest 6 years 2 months 12 days      
Aggregate intrinsic value of options exercisable $ 25.9      
Contractual term of options exercisable 5 years      
Unrecognized compensation relating to non-vested awards $ 5.3      
Unrecognized compensation relating to non-vested awards, recognition period (term) 1 year 4 months 24 days      
Unrecognized compensation relating to non-vested awards recognizable upon liquidity $ 23.2      
Aggregate intrinsic value of options exercised $ 4.8 2.5 2.1  
—PRSUs        
Share-based Compensation Arrangement by Share-based Payment Award        
Unrecognized compensation relating to non-vested awards, recognition period (term) 1 year 6 months      
Unrecognized compensation relating to non-vested awards other than option $ 14.7      
RSU's and PRSU's        
Share-based Compensation Arrangement by Share-based Payment Award        
Unrecognized compensation relating to non-vested awards, recognition period (term) 1 year 6 months      
Unrecognized compensation relating to non-vested awards other than option $ 14.7      
Aggregate intrinsic value of non options vested $ 12.3 $ 3.1 $ 0.6  
Omaha Topco Ltd. Stock Incentive Plan | Tranche 1        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 20.00%      
Omaha Topco Ltd. Stock Incentive Plan | Tranche 2        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 20.00%      
Omaha Topco Ltd. Stock Incentive Plan | Tranche 3        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 20.00%      
Omaha Topco Ltd. Stock Incentive Plan | Tranche 4        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 20.00%      
Omaha Topco Ltd. Stock Incentive Plan | Tranche 5        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 20.00%      
Omaha Topco Ltd. Stock Incentive Plan | —Tier I | —Share options        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 5 years      
Term of award 10 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 3 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 4 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 1 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 1 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 2 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 2 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 3 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 3 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Share options | Tranche 4 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 1 year      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Median        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 3 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 4 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Tranche 1        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Tranche 2        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —RSUs | Tranche 3        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs        
Share-based Compensation Arrangement by Share-based Payment Award        
Percentage of shares expected to vest upon achievement of average annual adjusted return on invested capital (percentage) 50.00%      
Percentage of shares expected to vest upon achievement of certain relative shareholders return (percentage) 50.00%      
Performance period 3 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 1 year      
Total number of shares expected to vest at term of award arrangement (percentage) 0.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Median        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 3 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 4 years      
Total number of shares expected to vest at term of award arrangement (percentage) 200.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Tranche 1        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Tranche 2        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —PRSUs | Tranche 3        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 1 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 1 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 2 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 2 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 3 | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 3 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —SARs | Tranche 4 | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 25.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Premium-priced options        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting period 3 years      
Term of award 10 years      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Premium-priced options | Tranche 1        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Premium-priced options | Tranche 2        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%      
Gates Industrial Corporation Plc 2018 Omnibus Incentive Plan | —Premium-priced options | Tranche 3        
Share-based Compensation Arrangement by Share-based Payment Award        
Vesting percentage 33.00%