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variety (711B)

      1 # Variety
      2 
      3 ## Variety of formal language
      4 
      5 Variety of [formal_language]s is closed under:
      6 - [Derivative]
      7 - [Boolean_operator]s ([union], [intersection], [complementation])
      8   - maybe not [complementation] in which case it is a [positive_variety]
      9 - and [inverse_morphism]
     10 
     11 ## Variety of [monoid]
     12 
     13 Variety of [monoid] is closed under [direct_product], [quotient], and [submonoid]
     14 
     15 ## Variety of [semigroup]
     16 
     17 We can impose that some elements in [equation]s are not mapped to the [neutral_element]
     18 - cf [non_erasing_morphism]
     19 
     20 ## Variety of [stamp]s
     21 
     22 - cf [length_preserving_morphism]
     23 
     24 ## Examples
     25 
     26 - [da]
     27 
     28 ## Types of variety
     29 
     30 - [Positive_variety]
     31 - [Variety_Li]
     32 
     33 Up: [algebraic_automata_theory]
     34 
     35 Aliases: varieties