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The class of morphisms of this category is an extension of the class of canonical (inserting the neutral element) morphisms ${\\rm BS}(s)\\hookrightarrow{\\rm BS}(s')$, where $s$ is a subsequence of $s'$. Every morphism of the new category induces a map between the $T$-fixed points but not necessarily between the whole varieties.\n  We construct a contravariant functor from this new category to the category of graded $H^\\bul"},"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":"1708.03611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-11T16:57:49Z","cross_cats_sorted":["math.AG","math.AT","math.CT"],"title_canon_sha256":"81efb352d3a90a29c855a667eda4992a7027d2f884539befcdca325e2b826d23","abstract_canon_sha256":"4556dea6daa781c6d27a22f7e12363226682741eb8ee620bc2fbdc2c56b14361"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:12.221024Z","signature_b64":"8cAns+NWi81UroAeaJ+Z10yzcBcGDuz7g2sHiqEqEFixKyroOUweSQkJgypS0fEFCb7WvVOYirFIKxklo/NSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9094ef7b401a8b3cc03f858f0041fde403582bddaaeef69655728e36c34efc9e","last_reissued_at":"2026-05-18T00:38:12.220402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:12.220402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categories of Bott-Samelson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.CT"],"primary_cat":"math.RT","authors_text":"Vladimir Shchigolev","submitted_at":"2017-08-11T16:57:49Z","abstract_excerpt":"We consider all Bott-Samelson varieties ${\\rm BS}(s)$ for a fixed connected semisimple complex algebraic group with maximal torus $T$ as the class of objects of some category. 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