Accumulated Other Comprehensive Income (Details) - Madison Industries IAQ Solutions Corporation - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2026	Mar. 31, 2025
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	$ 82.1	$ (92.5)
Reclassifications:
Total other comprehensive income (loss)	1.6	(3.7)
Ending balance	143.3	(43.0)
Accumulated Other Comprehensive Income (Loss)
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	(30.7)	(40.7)
Other comprehensive income (loss) before reclassifications	1.6	(6.6)
Reclassifications:
Realized gains - net	1.5	2.6
Income taxes	(1.3)	0.9
Total other comprehensive income (loss)	1.7	(3.1)
Ending balance	(29.0)	(43.9)
Accumulated Other Comprehensive Income (Loss) | Including Tax Distribution To Parent
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	(29.7)	(40.8)
Reclassifications:
Total other comprehensive income (loss)	1.8
Ending balance	(27.9)
Foreign Currency Translation
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	(24.4)	(39.7)
Other comprehensive income (loss) before reclassifications	(3.9)	0.4
Reclassifications:
Realized gains - net	0.0	0.0
Income taxes	0.0	0.0
Total other comprehensive income (loss)	(3.9)	0.4
Ending balance	(28.3)	(39.3)
Defined Benefit Plans
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	(3.6)	(5.5)
Other comprehensive income (loss) before reclassifications	0.1	0.0
Reclassifications:
Realized gains - net	0.0	0.0
Income taxes	0.0	0.0
Total other comprehensive income (loss)	0.1	0.0
Ending balance	(3.5)	(5.5)
Cash Flow Hedges
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	(1.7)	3.8
Other comprehensive income (loss) before reclassifications	5.4	(5.7)
Reclassifications:
Realized gains - net	1.5	1.5
Income taxes	(1.3)	0.9
Total other comprehensive income (loss)	5.6	(3.3)
Ending balance	3.9	0.5
Available-for-sale Securities
AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]
Beginning balance	0.0	0.6
Other comprehensive income (loss) before reclassifications	0.0	(1.3)
Reclassifications:
Realized gains - net	0.0	1.1
Income taxes	0.0	0.0
Total other comprehensive income (loss)	0.0	(0.2)
Ending balance	$ 0.0	$ 0.4