{"paper":{"title":"The core and dual core inverse of a morphism with factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Tingting Li","submitted_at":"2018-04-24T02:42:59Z","abstract_excerpt":"Let $\\mathscr{C}$ be a category with an involution $\\ast$. Suppose that $\\varphi : X \\rightarrow X$ is a morphism and $(\\varphi_1, Z, \\varphi_2)$ is an (epic, monic) factorization of $\\varphi$ through $Z$, then $\\varphi$ is core invertible if and only if $(\\varphi^{\\ast})^2\\varphi_1$ and $\\varphi_2\\varphi_1$ are both left invertible if and only if $((\\varphi^{\\ast})^2\\varphi_1, Z, \\varphi_2)$, $(\\varphi_2^{\\ast}, Z, \\varphi_1^{\\ast}\\varphi^{\\ast}\\varphi)$ and $(\\varphi^{\\ast}\\varphi_2^{\\ast}, Z, \\varphi_1^{\\ast}\\varphi)$ are all essentially unique (epic, monic) factorizations of $(\\varphi^{\\as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08817","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"}