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Lexicographic sums and fibre-faithful maps

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Abstract

The notion of lexicographic sum is introduced in general categories. Existence criteria are derived, particularly for locally cartesian closed categories and for categories with suitable coproducts. Lexicographic sums satisfy a generalized associative law. More importantly, every morphism can be factored through the lexicographic sum of its fibres. This factorization and the two types of maps arising from it, fibre-trivial and fibre-faithful, are studied particularly for partially ordered sets and forT 1-spaces.

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Börger, R., Tholen, W. & Tozzi, A. Lexicographic sums and fibre-faithful maps. Appl Categor Struct 1, 59–83 (1993). https://doi.org/10.1007/BF00872986

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Mathematics Subject Classifications (1991)

  • 18A30
  • 18A32
  • 18D10
  • 54B30
  • 06A99

Key words

  • Lexicographic sum
  • exponentiable point
  • disjoint points
  • fibre-faithful map
  • fibre-trivial map