

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.275291 
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. 