细微的差异
发表于 2025-3-25 05:41:58
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incite
发表于 2025-3-25 08:38:01
Free GroupsAs motivation for the general investigation of universal constructions, the concept of a free group on a set . is defined, and such groups are constructed in three ways: As sets of group-theoretic terms in . modulo consequences of the group identities, as subgroups of sufficiently large direct product groups, and as groups of reduced words.
绿州
发表于 2025-3-25 13:58:08
Varieties of AlgebrasWe at last formally define the concept of a (set-based) algebra, consider classes of algebras defined by families of identities (varieties), and prove Birkhoff’s . theorem. We devote several pages to Lie algebras. Clonal categories, and Lawvere’s Structure and Semantics functors, are briefly introduced.
Flat-Feet
发表于 2025-3-25 16:29:45
0172-5939 pen questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book..978-3-319-11477-4978-3-319-11478-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
撕裂皮肉
发表于 2025-3-25 23:42:47
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人类
发表于 2025-3-26 03:06:58
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Root494
发表于 2025-3-26 07:53:19
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Communal
发表于 2025-3-26 11:51:01
Lattices, Closure Operators, and Galois Connectionsound, and as algebraic structures, and various completeness conditions they can satisfy are examined.Such structures often arise from . on sets, and this concept is developed.An insufficiently well known source of closure operators, which we develop, is the concept of a . between two sets. In the ca
破布
发表于 2025-3-26 13:22:42
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SOBER
发表于 2025-3-26 17:08:13
Universal Constructions in Category-Theoretic Termsctors, adjoint functors and limits and colimits; how one of these constructions can often be expressed in terms of another, and when such constructions exist. We prove such results as that limits always “respect” other limits, and colimits other colimits, and also examine special but important situa