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The aim is to demonstrate the existence of injective envelopes for certain quantum algebras and categories.

July 6, 2026Studia MathematicaOpen Access

Injectivity for algebras and categories with quantum symmetry

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The aim is to demonstrate the existence of injective envelopes for certain quantum algebras and categories.
Established existence of injective envelopes for unital Yetter–Drinfeld C∗-algebras.
Analyzed bimodule categories over rigid C∗-tensor categories.
Investigated boundary actions of Drinfeld doubles of compact quantum groups.
Confirmed the existence of injective envelopes in the studied algebras and categories.
Proved that this existence implies monoidal invariance of boundary actions.
Demonstrated how these results relate to quantum symmetry in algebraic structures.

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Randomized trial establishes injective envelopes, showing monoidal invariance in quantum algebra structures.

Hataishi et al. (2026) studied this question.

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