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Temporary Equity and Equity - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions |  |  |  |  |  |  |  | 12 Months Ended |  |
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Sep. 09, 2021 | Jul. 01, 2021 | May 29, 2021 | Jan. 11, 2019 | Nov. 30, 2018 | Aug. 02, 2016 | Nov. 04, 2015 | Dec. 31, 2022 | Dec. 31, 2021 | Aug. 30, 2021 | Dec. 20, 2018
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Issuance of common stock (in shares) |  |  |  |  |  |  | 8,500,000 |  |  |  |
Preferred stock trading days to calculate volume weighted average price (at least) |  |  |  |  |  |  |  | 20 days |  |  |
Additional share consideration |  |  |  |  |  |  |  |  | $ 0.3 |  |
Preferred stock |  |  |  |  |  |  |  | $ 17.6 | $ 18.8 |  |
Proceed from exchange for accrued and unpaid dividend |  | $ 0.3 |  |  |  |  |  |  |  |  |
Preferred stock cumulative cash dividend rate |  |  |  |  |  |  |  | 7.50% |  |  |
Preferred stock dividend rate |  |  |  |  |  |  |  | 4.00% |  |  |
Accreting dividend threshold rate |  |  |  |  |  |  |  | 7.25% |  |  |
Volume weighted average price threshold percentage |  |  |  |  |  |  |  | 150.00% |  |  |
Preferred stock force conversion, trading days to calculate volume weighted average price |  |  |  |  |  |  |  | 30 days |  |  |
Consent rights percentage (at least) |  |  |  |  |  |  |  | 75.00% |  |  |
Par value (in usd per share) |  |  |  |  |  |  |  | $ 0.001 | $ 0.001 |  |
Tax Benefits Preservation Plan, outstanding shares ownership threshold (percent) |  |  |  |  |  |  |  |  |  | 4.90% |
Rights to common stockholders threshold period | 10 days |  |  |  |  |  |  |  |  |  |
Innovate Corp |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Beneficial ownership percentage | 4.90% |  |  |  |  |  |  |  |  |  |
Maximum |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock dividend rate |  |  |  |  |  |  |  | 2.00% |  |  |
Minimum |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock dividend rate |  |  |  |  |  |  |  | 0.00% |  |  |
Series A shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Shares issued (in shares) |  |  |  |  |  |  |  | 41,820.25 |  |  |
Preferred stock conversion price (in usd per share) |  |  |  |  |  |  |  | $ 3.52 |  |  |
Shares reserved for issuance (in shares) |  |  |  |  |  |  |  | 500,000 |  |  |
Par value (in usd per share) |  |  |  |  |  |  |  | $ 0.001 |  |  |
Series A-2 shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock conversion price (in usd per share) |  |  |  |  |  |  |  | 5.33 |  |  |
Series A-3 Preferred Stock |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock conversion price (in usd per share) |  |  |  |  |  |  |  | $ 4.25 |  |  |
Number of shares to be issued upon conversion of preferred stock (in shares) |  |  |  |  |  |  |  | 1,740,700 |  |  |
Series A-4 Preferred Stock |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock conversion price (in usd per share) |  |  |  |  |  |  |  | $ 8.25 |  |  |
Number of shares to be issued upon conversion of preferred stock (in shares) |  |  |  |  |  |  |  | 1,875,533 |  |  |
Series A-4 shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock conversion price (in usd per share) | $ 10 |  |  |  |  |  |  |  |  |  |
Par value (in usd per share) | $ 0.001 |  |  |  |  |  |  |  |  |  |
Preferred stock purchase price (in usd per share) | 20.00 |  |  |  |  |  |  |  |  |  |
Common stock |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Redemption of preferred stock |  |  | $ 10.4 |  |  |  |  |  |  |  |
Number of shares of common stock from conversion (in shares) |  |  | 50,410 |  |  |  |  |  |  |  |
CGIC |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Redemption value |  | $ 16.1 |  |  |  |  |  |  |  |  |
CGIC | Series A shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Shares issued (in shares) |  | 6,125 |  |  |  |  |  |  |  |  | 6,125
Stock repurchase program, number of shares expected to be redeemed (in shares) |  |  | 6,125 |  |  |  |  |  |  |  |
CGIC | Series A-2 shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Issuance of common stock (in shares) |  | 10,000 |  | 10,000 |  |  |  |  |  |  |
Stock repurchase program, number of shares expected to be redeemed (in shares) |  |  | 10,000 |  |  |  |  |  |  |  |
DBMGi |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock, initial dividend rate period |  |  |  |  |  |  |  | 5 years |  |  |
Preferred stock, dividend, paid in kind percentage |  |  |  |  |  |  |  | 9.00% |  |  |
Preferred stock, dividend paid in cash, percentage |  |  |  |  |  |  |  | 8.25% |  |  |
DBMGi | LIBOR |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock, dividend, basis spread on variable rate |  |  |  |  |  |  |  | 5.85% |  |  |
DBMGi | Paid In Kind |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock, dividend, basis spread on variable rate |  |  |  |  |  |  |  | 0.75% |  |  |
DBMGi | Series A shares issued and outstanding | Discontinued Operations | CIG |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Proceeds from divestiture of businesses |  | $ 40.9 |  |  |  |  |  |  |  |  |
DBMGi | Series A shares issued and outstanding | Consolidation, Eliminations |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Issuance of common stock (in shares) |  |  |  |  | 40,000 |  |  |  |  |  |
Luxor Capital Partners L P Member | Series A shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Conversion of stock, number of shares (in shares) |  |  |  |  |  |  |  |  | 119,784 |  |
Luxor Capital Partners L P Member | Series A1 Preferred Stock |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Issuance of common stock (in shares) |  |  |  |  |  | 9,000 |  |  |  |  |
Corrib Master Fund Ltd. Member | Series A shares issued and outstanding |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Issuance of common stock (in shares) |  |  |  |  |  | 1,000 |  |  |  |  |
Conversion of stock, number of shares (in shares) |  |  |  |  |  |  |  |  | 13,477 |  |
Corrib Master Fund Ltd. and Luxor Capital Partners L P Member |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Preferred stock trading days to calculate volume weighted average price (at least) |  |  |  |  |  |  |  | 30 days |  |  |
Volume weighted average price threshold period |  |  |  |  |  |  |  | 2 days |  |  |
Common stock, accrued value percent |  |  |  |  |  |  |  | 0.01875 |  |  |

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- Definition Preferred Stock, Dividend, Paid In Kind, Percentage + References No definition available. + Details
Name: | vate_PreferredStockDividendPaidInKindPercentage
Namespace Prefix: | vate_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition This element represents the Preferred Stock force conversion trading period used to calculate volume weighted average price. + References No definition available. + Details
Name: | vate_PreferredStockForceConversionTradingPeriodToCalculateVolumeWeightedAveragePrice
Namespace Prefix: | vate_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition Preferred Stock, Initial Dividend Rate Period + References No definition available. + Details
Name: | vate_PreferredStockInitialDividendRatePeriod
Namespace Prefix: | vate_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition Preferred Stock Purchase Price + References No definition available. + Details
Name: | vate_PreferredStockPurchasePrice
Namespace Prefix: | vate_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition This element represents the Preferred Stock trading period used to calculate volume weighted average price. + References No definition available. + Details
Name: | vate_PreferredStockTradingPeriodToCalculateVolumeWeightedAveragePrice
Namespace Prefix: | vate_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition Proceed From Exchange For Accrued And Unpaid Dividend + References No definition available. + Details
Name: | vate_ProceedFromExchangeForAccruedAndUnpaidDividend
Namespace Prefix: | vate_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

X
- Definition Rights To Common Stock Holders Threshold Period + References No definition available. + Details
Name: | vate_RightsToCommonStockHoldersThresholdPeriod
Namespace Prefix: | vate_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Definition Tax Benefits Preservation Plan, Outstanding Shares Ownership Threshold + References No definition available. + Details
Name: | vate_TaxBenefitsPreservationPlanOutstandingSharesOwnershipThreshold
Namespace Prefix: | vate_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | instant

X
- Definition This element represents the percentage threshold of volume weighted average price. + References No definition available. + Details
Name: | vate_VolumeWeightedAveragePriceThresholdPercentage
Namespace Prefix: | vate_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Volume Weighted Average Price Threshold Period + References No definition available. + Details
Name: | vate_VolumeWeightedAveragePriceThresholdPeriod
Namespace Prefix: | vate_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis=vate_InnovateCorpMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RangeAxis=srt_MaximumMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RangeAxis=srt_MinimumMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_SeriesAPreferredStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=vate_SeriesATwoPreferredStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=vate_SeriesA3PreferredStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=vate_SeriesA4PreferredStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_SeriesBPreferredStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_CommonStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_CounterpartyNameAxis=vate_CGIMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_CounterpartyNameAxis=vate_DBMGiMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_VariableRateAxis=us-gaap_LondonInterbankOfferedRateLIBORMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_VariableRateAxis=vate_PaidInKindMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_DisposalGroupClassificationAxis=us-gaap_SegmentDiscontinuedOperationsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis=vate_CGICMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_ConsolidationItemsAxis=srt_ConsolidationEliminationsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_CounterpartyNameAxis=vate_LuxorCapitalPartnersLPMemberMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=vate_SeriesA1PreferredStockMemberMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_CounterpartyNameAxis=vate_CorribMasterFundLtdMemberMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_CounterpartyNameAxis=vate_CorribMasterFundLtdAndLuxorCapitalPartnersLPMemberMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |