Corepresentations of Rota–Baxter Turaev’s group coalgebras

Following Ma et al.’s work on Rota–Baxter T-(co)algebras [J. Geom. Phys. 175 (2022) 104469], in this paper, we continue to study the corepresentation theory of Rota–Baxter T-coalgebras and introduce the notion of Rota–Baxter T-comodules and investigate their properties. Moreover, we investigate the relations among some related T-comodules structures (such as dendriform T-comodules, pre-Lie T-comodules), and at last give some examples of Rota–Baxter T-comodules.