研究者情報 | 神奈川大学

タケヤマ　マコト Takeyama Makoto 武山　誠所属神奈川大学理学部情報科学科神奈川大学大学院理学研究科理学専攻（情報科学領域）職種教授
言語種別	英語
発行・発表の年月	1999
形態種別	学術雑誌
査読	査読あり
標題	Sketches
執筆形態	共著
掲載誌名	J.Pure and Applied Algebra,vol.143
掲載区分	国外
巻・号・頁	143,pp.275-291
著者・共著者	Yoshili Kinoshita, John Power, Makoto Takeyama
概要	We generalise the notion of sketch. For any locally finitely presentable category, one can speak of algebraic structure on the category, or equivalently, a finitary monad on it. For any such finitary monad, we define the notions of sketch and strict model and prove that any sketch has a generic strict model on it. This is all done with enrichment in any monoidal biclosed category that is locally finitely presentable as a closed category. Restricting our attention to enrichment in Cat, we mildly extend the definition of strict model to give a definition of model, and we prove that every sketch has a generic model on it. The leading example is the category of small categories together with the monad for small categories with finite products: we then recover the usual notions of finite product sketch and model; and that is typical. This generalises many of the extant notions of sketch.