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Leases - Schedule of Maturities Lease Liabilities Weighted-Average Remaining Term and Weighted-Average Discount Rate (Parenthetical) (Details) $ in Millions	Mar. 31, 2023 USD ($)
Leases [Abstract]
Legally binding minimum lease payments for leases not yet commenced	$ 5.5

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- Definition

Minimum Lease Payments for Leases Not Yet Commenced

+ References

No definition available.

+ Details

Name:	tyra_MinimumLeasePaymentsForLeasesNotYetCommenced
Namespace Prefix:	tyra_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

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- References

No definition available.

+ Details

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