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We construct a Frobenius exact subcategory $\\mathcal{GP}(\\mathcal{G}_P\\operatorname{proj}(\\mathcal{B}^{\\mathcal{C}}))$ of the functor category $\\mathcal{B}^{\\mathcal{C}}$, and we show that it is a subcategory of the Gorenstein projective objects $\\mathcal{GP}(\\mathcal{B}^{\\mathcal{C}})$ in $\\mathcal{B}^{\\mathcal{C}}$. Furthermore, we obtain criteria for when $\\mathcal{GP}(\\mathcal{G}_P\\operatorname{proj}(\\mathcal{B}^{\\mathcal{C}}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.05493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-01-16T21:55:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"4169e03a07cf73eaf8420b640a214c4fe731b663ab58de7faf9145e8be220cfe","abstract_canon_sha256":"5417fa3d9036020e9c6cbf42123eebd393fce002ec9f1b718331375d0771ce0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:15.375926Z","signature_b64":"phobKl6A49LzSiA/9SP+/tvHrTG4jvypQbflJBOPYAWAKYbUoMtnPRkZyLFTf3A4nWFlEb2g3kPE+ut6TVnYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5bcee4fe771b96402ac07d64ace9e66a279873654fd030daae988fa785558be","last_reissued_at":"2026-05-17T23:56:15.375382Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:15.375382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gorenstein projective objects in functor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Sondre Kvamme","submitted_at":"2018-01-16T21:55:10Z","abstract_excerpt":"Let $k$ be a commutative ring, let $\\mathcal{C}$ be a small, $k$-linear, Hom-finite, locally bounded category, and let $\\mathcal{B}$ be a $k$-linear abelian category. 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