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Summary of Significant Accounting Policies - Additional Information (Details) - USD ($) $ in Millions	Sep. 30, 2023	Dec. 31, 2022
Significant Accounting Policies [Line Items]
Restricted Cash	$ 1.0	$ 1.0

X

- Definition

Significant Accounting Policies.

+ References

No definition available.

+ Details

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Namespace Prefix:	tyra_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of cash restricted as to withdrawal or usage. Cash includes, but is not limited to, currency on hand, demand deposits with banks or financial institutions, and other accounts with general characteristics of demand deposits.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-8

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(1)(a))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479853/942-210-S99-1

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant