{"paper":{"title":"On the Morphisms and Transformations of Tsuyoshi Fujiwara (as a concretion of a bidimensional many-sorted general algebra and its application to the equivalence between many-sorted clones and algebraic theories)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Juan Climent Vidal, Juan Soliveres Tur","submitted_at":"2012-01-25T11:34:32Z","abstract_excerpt":"For single-sorted algebras, Fujiwara defined, through the concept of family of basic mapping-formulas, a notion of morphism which generalizes the ordinary notion of homomorphism between algebras and an equivalence relation, the conjugation, on the families of basic mapping-formulas, which corresponds to the relation of inner isomorphism for algebras. In this paper we extend the theory of Fujiwara about morphisms to the many-sorted algebras, by defining the concept of polyderivor between many-sorted signatures, which assigns to basic sorts, words and to formal operations, families of derived te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5239","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"}