doi:10.1142/S0219498827501234engArenas, ManuelLabra, AliciaPaniello, IreneIn-evolution operators in Lotka-Volterra coalgebrasART-2026-147968In this paper, we study properties of in-evolution operators in Lotka–Volterra coalgebras. First, we cope with the notion of coalgebra character, and classify characters in special cases as, for instance, those of two-dimensional Lotka–Volterra coalgebras and of normalized duals of Lotka–Volterra algebras. Then, we study the in-evolution operators defined by nonzero characters of Lotka–Volterra coalgebras, focusing on the case when the in-evolution operators are stochastic maps. For such operators, we study the usual equilibrium issues, paying special attention to idempotent in-evolution operators, and the information that their idempotency provides on the structure of Lotka–Volterra coalgebras.2026http://zaguan.unizar.es/record/17046410.1142/S0219498827501234http://zaguan.unizar.es/record/170464oai:zaguan.unizar.es:170464info:eu-repo/grantAgreement/ES/DGA/E22-23Rinfo:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21JOURNAL OF ALGEBRA AND ITS APPLICATIONS 2750123 (2026), 26All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess