Compendium of Predicates
  • 🌐Orientation
    • ⭐Welcome
    • āœ’ļøNotation
    • šŸ˜…An Example
  • 🧰Definitions
    • Relation Taxonomy
    • Order Taxonomy
    • Algebra
      • Magma
      • Semigroup
      • Monoid
      • Group
      • Ringoid
      • Semiring
      • Ring
      • Unit Ring
      • Boolean Ring
      • Boolean Group
    • Bandler and Kohout Products of Relations
    • Closed
    • Complement
    • De Baets and Kerre Products of Relations
    • Extremal Elements
    • Galois Connection
    • Images of a set under a relation
    • Indexed Union and Intersection
    • Monoidal Preorder
    • Monotone Map
    • Natural Projection
    • Non-Preservation of Extrema
    • Over and Under
    • Power Set
    • Preorder
    • Preservation of Extrema
    • Product
    • Relation Inclusion
    • Row Constant Relations
    • Semilattice
    • Set Inclusion
    • Symmetric Monoidal Preorder
    • Upper Set
  • šŸ”¬Checks
    • šŸŽ™ļøA few words about the checks
    • Indirect Equality and Inclusion
    • Below
    • Extremal Elements
    • Relation Division
    • Algebra
      • Ring
      • Boolean Ring
      • Boolean Group
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  1. Definitions

Symmetric Monoidal Preorder

SymmetricMonoidalPreorderā€…ā€ŠXā€…ā€ŠRā€…ā€ŠāŠ—ā€…ā€ŠI\textbf{SymmetricMonoidalPreorder} \; X \; R \; \otimes \; ISymmetricMonoidalPreorderXRāŠ—I

MonoidalPreorderā€…ā€ŠXā€…ā€ŠRā€…ā€ŠāŠ—ā€…ā€ŠI\textbf{MonoidalPreorder} \; X \; R \; \otimes \; IMonoidalPreorderXRāŠ—I

Symmetricā€…ā€ŠXā€…ā€ŠāŠ—\textbf{Symmetric} \; X \; \otimesSymmetricXāŠ—


pred SymmetricMonoidalPreorder(X: set univ, R: univ->univ, op: univ->univ->univ, I: univ) {
  MonoidalPreorder[X,R,op,I]
  Symmetric[X,op]
}

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Last updated 1 year ago

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