East, JamesFresacher, MatthiasAzeef Muhammed, P. A.Stokes, Tim E.2026-11-062026-11-062026East, J., Fresacher, M., Azeef Muhammed, P. A., & Stokes, T. (2026). Categorical representation of DRC-semigroups. Journal of Algebra, 691, 230-291. https://doi.org/10.1016/j.jalgebra.2025.11.0060021-8693https://hdl.handle.net/10289/18745DRC-semigroups model associative systems with domain and range operations, and contain many important classes, such as inverse, restriction, Ehresmann, regular ⁎-, and ⁎-regular semigroups; concrete examples include diagram monoids, linear monoids, relation monoids, among many others. In this paper we show that the category of DRC-semigroups is isomorphic to a category of certain biordered categories whose object sets are projection algebras in the sense of Jones. This extends the recent groupoid approach to regular ⁎-semigroups of the first and third authors. We also establish the existence of free DRC-semigroups by constructing a left adjoint to the forgetful functor into the category of projection algebras.enRe-use licence for this version: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalbiordered categoryDRC-semigroupmathematicsprojection algebraJournal Article10.1016/j.jalgebra.2025.11.0061090-266X4904 Pure Mathematics49 Mathematical Sciences4902 Mathematical physics4904 Pure mathematics