Tortuous
发表于 2025-3-27 00:20:53
Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints . of algebras has a left adjoint if and only if it is represented by a .. of .. Using this approach, descriptions of all such functors from monoids to monoids, and from . -modules to .-modules for arbitrary rings . and ., are obtained. Some general restrictions on representable functors are noted (
Glower
发表于 2025-3-27 05:02:03
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不溶解
发表于 2025-3-27 07:24:59
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惊惶
发表于 2025-3-27 10:09:41
,Die Messung der Produktivität,t and right universal constructions), similar constructions for monoids, rings, and Boolean rings, and constructions connecting one sort of structure to another (e.g., abelianizations of groups). For perspective, we also look at the topological constructions of Stone-Čech compactification, and of universal covering spaces.
种族被根除
发表于 2025-3-27 16:08:26
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阴郁
发表于 2025-3-27 17:45:18
Lattices, Closure Operators, and Galois Connectionsse for which the concept was named, the two sets are, respectively, the elements of a finite separable normal field extension, and the automorphisms of that extension. Another of the many examples noted relates the set of models of a formal language, and the set of propositions in that language.
捕鲸鱼叉
发表于 2025-3-28 01:51:01
Universal Constructions in Category-Theoretic Termstions where limits and colimits respect one another. (For instance, in the category of sets, though not in a general category, direct limits respect finite products. This is why, given a directed system of finitary algebras, one gets an induced algebra structure on the direct limit of their underlying sets.)
开头
发表于 2025-3-28 05:57:05
Algebra and Coalgebra Objects in Categories, and Functors Having Adjointswhich show, for instance, that there can be no such nontrivial functors from semigroups to monoids, or from groups to unital rings). We examine briefly . representable functors among varieties of algebras, noting some open questions about these.
Radiculopathy
发表于 2025-3-28 10:20:15
Die informatisierte Service-Ökonomiese for which the concept was named, the two sets are, respectively, the elements of a finite separable normal field extension, and the automorphisms of that extension. Another of the many examples noted relates the set of models of a formal language, and the set of propositions in that language.
Glower
发表于 2025-3-28 11:40:44
Christian Arnold,Hermann Knödlertions where limits and colimits respect one another. (For instance, in the category of sets, though not in a general category, direct limits respect finite products. This is why, given a directed system of finitary algebras, one gets an induced algebra structure on the direct limit of their underlying sets.)