Amount of impairment loss for asset. Includes, but is not limited to, tangible and intangible assets and goodwill.

Name:	us-gaap_AssetImpairmentCharges
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of costs incurred to date for the specified restructuring cost.

+ References

+ Details

Name:	us-gaap_RestructuringAndRelatedCostCostIncurredToDate1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount expected to be recognized in earnings for the specified restructuring cost.

+ References

+ Details

Name:	us-gaap_RestructuringAndRelatedCostExpectedCost1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of expenses associated with exit or disposal activities pursuant to an authorized plan. Excludes expenses related to a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 55
-Paragraph 18
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476153/220-40-55-18

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.b.1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482047/420-10-45-3

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 5.P.3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 21
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476148/220-40-50-21

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476148/220-40-50-6

+ Details

Name:	us-gaap_RestructuringCharges
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.b.1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.b.2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

+ Details

Name:	us-gaap_RestructuringCostAndReserveLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of restructuring charges, remediation cost, and asset impairment loss.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_RestructuringSettlementAndImpairmentProvisions
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	srt_ConsolidationItemsAxis=us-gaap_MaterialReconcilingItemsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=matv_FAMSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ConsolidationItemsAxis=us-gaap_OperatingSegmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=matv_SASSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_EmployeeSeveranceMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_OtherRestructuringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_FacilityClosingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Restructuring and Other Impairment Activities - Schedule of Total Restructuring, Restructuring Related, and Impairment Expense (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jun. 30, 2026	Jun. 30, 2025	Jun. 30, 2026	Jun. 30, 2025
Restructuring Cost and Reserve [Line Items]
Restructuring charges	$ 0.7	$ 3.8	$ 1.9	$ 4.8
Total restructuring and other impairment expense	0.7	3.8	2.0	10.1
Unallocated
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.0	1.4	0.0	1.4
Filtration and Advanced Materials
Restructuring Cost and Reserve [Line Items]
Other impairment expense	0.0	0.0	0.1	5.3
Filtration and Advanced Materials \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.7	2.2	1.9	2.9
Sustainable and Adhesive Solutions \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.0	0.2	0.0	0.5
Severance and termination benefits \| Unallocated
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.0	1.4	0.0	1.4
Severance and termination benefits \| Filtration and Advanced Materials \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.1	1.8	0.1	2.1
Severance and termination benefits \| Sustainable and Adhesive Solutions \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.0	0.2	0.0	0.4
Other exit costs \| Filtration and Advanced Materials \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.6	0.4	1.8	0.8
Other exit costs \| Sustainable and Adhesive Solutions \| Operating Segments
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.0	0.0	0.0	$ 0.1
Closed Facility \| Filtration and Advanced Materials
Restructuring Cost and Reserve [Line Items]
Restructuring charges	0.6	$ 1.8
Restructuring incurred to date	12.7		12.7
Restructuring expected cost	$ 1.5		$ 1.5