{"paper":{"title":"Core and Dual Core Inverses of a Sum of Morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Jianlong Chen, Sanzhang Xu, Tingting Li","submitted_at":"2016-12-26T07:37:59Z","abstract_excerpt":"Let $\\mathscr{C}$ be an additive category with an involution $\\ast$. Suppose that $\\varphi : X \\rightarrow X$ is a morphism of $\\mathscr{C}$ with core inverse $\\varphi^{\\co} : X \\rightarrow X$ and $\\eta : X \\rightarrow X$ is a morphism of $\\mathscr{C}$ such that $1_X+\\varphi^{\\co}\\eta$ is invertible. Let $\\alpha=(1_X+\\varphi^{\\co}\\eta)^{-1},$ $\\beta=(1_X+\\eta\\varphi^{\\co})^{-1},$ $\\varepsilon=(1_X-\\varphi\\varphi^{\\co})\\eta\\alpha(1_X-\\varphi^{\\co}\\varphi),$ $\\gamma=\\alpha(1_X-\\varphi^{\\co}\\varphi)\\beta^{-1}\\varphi\\varphi^{\\co}\\beta,$ $\\sigma=\\alpha\\varphi^{\\co}\\varphi\\alpha^{-1}(1_X-\\varphi\\var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09482","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}