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In this paper, we address the question of when two corings in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules are Quillen equivalent.\n  The category of comodules over the trivial coring (A,A) is isomorphic to the category of A-modules, so the question above englobes that of "},"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":"1411.6517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-24T16:36:07Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"590201dc42834bd743fbc231f4e2a0e5f765949673c51cb7f0e6583529a5bdfb","abstract_canon_sha256":"375a8b374195b0da8ebd5ea62a3071cbfd8d13e80e0716dc403c94c57421b818"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:29.567925Z","signature_b64":"fnyWy+Psrtfsre96UhHE97SHYR+tmllqEK3VqxAlGf9kHZEpCK+NqJzWxQdqmU7DS+fxqs5aJl+ZfI+4Wh0ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59ae48dfd886f2b9ce094539fdfb1760163d7c0d1fa33fa3e9bc25438f911e42","last_reissued_at":"2026-05-18T01:23:29.567286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:29.567286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopical Morita theory for corings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.AT","authors_text":"Alexander Berglund, Kathryn Hess","submitted_at":"2014-11-24T16:36:07Z","abstract_excerpt":"A coring (A,C) consists of an algebra A and a coalgebra C in the monoidal category of A-bimodules. 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