標(biāo)題: Titlebook: Categories for the Working Mathematician; Saunders Mac Lane Textbook 19711st edition Springer Science+Business Media New York 1971 Adjoint [打印本頁] 作者: cucumber 時間: 2025-3-21 19:57
書目名稱Categories for the Working Mathematician影響因子(影響力)
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書目名稱Categories for the Working Mathematician網(wǎng)絡(luò)公開度
書目名稱Categories for the Working Mathematician網(wǎng)絡(luò)公開度學(xué)科排名
書目名稱Categories for the Working Mathematician被引頻次
書目名稱Categories for the Working Mathematician被引頻次學(xué)科排名
書目名稱Categories for the Working Mathematician年度引用
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書目名稱Categories for the Working Mathematician讀者反饋
書目名稱Categories for the Working Mathematician讀者反饋學(xué)科排名
作者: agonist 時間: 2025-3-21 22:54 作者: manifestation 時間: 2025-3-22 01:18 作者: 含糊其辭 時間: 2025-3-22 07:41 作者: 鋼筆記下懲罰 時間: 2025-3-22 11:38 作者: jaunty 時間: 2025-3-22 13:33
Adjoints,s. As motivation, we first reexamine the construction (§III.1) of a vector space . with basis .. For a fixed field . consider the functors . where, for each vector space W, U(W) is the set of all vectors in ., so that . is the forgetful functor, while, for any set ., .(.) is the vector space with basis ..作者: jaunty 時間: 2025-3-22 19:35
Daniele Di Castro,Giuseppe Balestrino of arrows. Each arrow .: . → . represents a function; that is, a set ., a set ., and a rule . ? . which assigns to each element . ∈ . an element . ∈ .; whenever possible we write . and not .(.), omitting unnecessary parentheses.作者: exceed 時間: 2025-3-23 00:45 作者: 使隔離 時間: 2025-3-23 04:13
Daniele Di Castro,Giuseppe Balestrinoctor, or as universal elements of a set-valued functor. Each universal determines a representation of a corresponding set-valued functor as a hom-functor. Such representations, in turn, are analyzed by the Yoneda Lemma. Limits are an important example of universals — both the inverse limits (= proje作者: 過份 時間: 2025-3-23 09:18
Soumaya Yacout,Vahid Ebrahimipours. As motivation, we first reexamine the construction (§III.1) of a vector space . with basis .. For a fixed field . consider the functors . where, for each vector space W, U(W) is the set of all vectors in ., so that . is the forgetful functor, while, for any set ., .(.) is the vector space with ba作者: 闡釋 時間: 2025-3-23 12:11
Diseases of the Vagina and Urethra,egory . of all algebras of the given type, the forgetful functor .: . →., and its left adjoint ., which assigns to each set . the free algebra . of type . generated by elements of .. A trace of this adjunction <., ., ?>: . ? . resides in the category .; indeed, the composite .=. is a functor . → ., 作者: 使無效 時間: 2025-3-23 15:06
https://doi.org/10.1007/978-3-319-15422-0d by the usual diagrams relative to the cartesian product × in ., while a ring is a monoid in ., relative to the tensor product ? there. Thus we shall begin with categories . equipped with a suitable bifunctor such as × or ?, more generally denoted by □. These categories will themselves be called “m作者: Ccu106 時間: 2025-3-23 19:41 作者: altruism 時間: 2025-3-24 00:26
Drugs and Breastfeeding: The Knowledge Gap defining such an extension. However, if . is a subcategory of ., each functor .:. → . has in principle . canonical (or extreme) “extensions” from . to functors ., .: . → .. These extensions are characterized by the universality of appropriate natural transformations; they need not always exist, but作者: Spina-Bifida 時間: 2025-3-24 04:55 作者: 沒血色 時間: 2025-3-24 08:16 作者: stress-response 時間: 2025-3-24 11:30 作者: Patrimony 時間: 2025-3-24 17:58
Daniele Di Castro,Giuseppe Balestrino of arrows. Each arrow .: . → . represents a function; that is, a set ., a set ., and a rule . ? . which assigns to each element . ∈ . an element . ∈ .; whenever possible we write . and not .(.), omitting unnecessary parentheses.作者: 線 時間: 2025-3-24 19:24
https://doi.org/10.1007/978-3-319-14478-8n a set-theoretical basis in the next section. Hence for this section a category will not be described by sets (of objects and of arrows) and functions (domain, codomain, composition) but by axioms as in §I.1.作者: cauda-equina 時間: 2025-3-24 23:17
Soumaya Yacout,Vahid Ebrahimipours. As motivation, we first reexamine the construction (§III.1) of a vector space . with basis .. For a fixed field . consider the functors . where, for each vector space W, U(W) is the set of all vectors in ., so that . is the forgetful functor, while, for any set ., .(.) is the vector space with basis ..作者: invade 時間: 2025-3-25 06:41 作者: 彎曲的人 時間: 2025-3-25 08:15 作者: 石墨 時間: 2025-3-25 15:23
Challenges in Pediatric Oral DosingThis chapter covers two useful types of limits (and colimits): The filtered limits, which are limits taken over preordered sets which are directed (and, more generally, over certain filtered categories), and the “ends”, which are limits obtained from certain bifunctors, and which behave like integrals.作者: miniature 時間: 2025-3-25 17:49 作者: forbid 時間: 2025-3-25 20:23
Limits,This chapter examines the construction and properties of limits, as well as the relation of limits to adjoints. This relation is then used in the basic existence theorems for adjoint functors, which give universals and adjoints in a wide variety of cases. The chapter closes with some indications of the uses of adjoint functors in topology.作者: 戲法 時間: 2025-3-26 03:35
Special Limits,This chapter covers two useful types of limits (and colimits): The filtered limits, which are limits taken over preordered sets which are directed (and, more generally, over certain filtered categories), and the “ends”, which are limits obtained from certain bifunctors, and which behave like integrals.作者: defenses 時間: 2025-3-26 05:26 作者: confederacy 時間: 2025-3-26 08:52 作者: APO 時間: 2025-3-26 14:05 作者: ingrate 時間: 2025-3-26 18:00 作者: Morsel 時間: 2025-3-26 21:10
Monads and Algebras,egory . of all algebras of the given type, the forgetful functor .: . →., and its left adjoint ., which assigns to each set . the free algebra . of type . generated by elements of .. A trace of this adjunction <., ., ?>: . ? . resides in the category .; indeed, the composite .=. is a functor . → ., 作者: 晚間 時間: 2025-3-27 02:52
Monoids,d by the usual diagrams relative to the cartesian product × in ., while a ring is a monoid in ., relative to the tensor product ? there. Thus we shall begin with categories . equipped with a suitable bifunctor such as × or ?, more generally denoted by □. These categories will themselves be called “m作者: Canary 時間: 2025-3-27 07:31 作者: Override 時間: 2025-3-27 11:59
Kan Extensions, defining such an extension. However, if . is a subcategory of ., each functor .:. → . has in principle . canonical (or extreme) “extensions” from . to functors ., .: . → .. These extensions are characterized by the universality of appropriate natural transformations; they need not always exist, but作者: 團(tuán)結(jié) 時間: 2025-3-27 15:24
Textbook 19711st edition in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with a作者: incarcerate 時間: 2025-3-27 18:10 作者: FRET 時間: 2025-3-27 23:22 作者: 懸崖 時間: 2025-3-28 06:07 作者: gusher 時間: 2025-3-28 07:38 作者: 我不死扛 時間: 2025-3-28 12:36 作者: Vaginismus 時間: 2025-3-28 17:15 作者: 極大痛苦 時間: 2025-3-28 22:03
Kan Extensions,damental concepts in category theory. With them we find again that each fundamental concept can be expressed in terms of the others. This chapter begins by expressing adjoints as limits and ends by expressing “everything” as Kan extensions.作者: Hearten 時間: 2025-3-29 00:09 作者: Debrief 時間: 2025-3-29 06:44 作者: 鴕鳥 時間: 2025-3-29 09:19
Monads and Algebras,is monad in .. Another principal result is a theorem due to Beck, which describes exactly those categories . with adjunctions <., ., ?>: . ? . which can be so reconstructed from a monad . in the base category .. It then turns out that algebras in this last sense are so general as to include the compact Hausdorff spaces (§ 9).作者: caldron 時間: 2025-3-29 14:49
Monoids,spaces by this isomorphism. Closer analysis shows that more care is requisite in this identification — one must use the . isomorphism, and one must verify that the resulting identification of multiple products can be made in a “coherent” way.作者: effrontery 時間: 2025-3-29 18:48
10樓作者: FUSE 時間: 2025-3-29 20:17
10樓
