Monoids, acts and categories with applications to wreath products and graphs : a handbook for students and researchers

by Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev

[目次]

  • Elementary properties of monoids, acts and categories: sets and relations
  • groupoids, semigroups and monoids
  • some classes of semigroups
  • acts over monoids (monoid automata)
  • decompositions and components
  • categories
  • functors. Constructions: products and coproducts
  • pullbacks and pushouts
  • free objects and generators
  • cofree objects and generators
  • tensor products
  • wreath products of monoids and acts
  • the wreath product of a monoid with a small category. Classes of acts: injective acts
  • divisible acts
  • principally weakly injective acts
  • fg-weakly injective acts
  • absolutely pure acts
  • cogenerators and overview
  • torsion free acts
  • flatness of acts and related properties
  • principally weakly flat acts
  • weakly flat acts
  • flat acts
  • acts satisfying condition (P)
  • acts satisfying condition (E)
  • equalizer flat acts
  • pullback flat acts and overview
  • projective acts
  • generators
  • regular acts and overview. Homological classification of monoids: principal weak injectivity
  • on fg-weak injectivity
  • weak injectivity
  • absolute purity
  • injectivity and overview
  • torsion freeness and principal weak flatness
  • flatness
  • condition (P)
  • strong flatness
  • projectivity
  • projective generators
  • freeness and overview
  • regularity of acts. Equivalence and duality: adjoint functors
  • categories equivalent to act - S Morita equivalence of monoids
  • endomorphism monoids of generators
  • on morita duality.

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この本の情報

書名 Monoids, acts and categories with applications to wreath products and graphs : a handbook for students and researchers
著作者等 Kilʹp, M.
Knauer, U.
Mikhalev, A. V.
Knauer Ulrich
Mikhalev A. V.
Kilp Mati
シリーズ名 De Gruyter expositions in mathematics
出版元 Walter de Gruyter
刊行年月 2000
ページ数 xvii, 529 p
大きさ 25 cm
ISBN 3110152487
NCID BA46217376
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言語 英語
出版国 ドイツ
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