Mario Román

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Polar shuffles

Polar shuffles

Aug 14, 20231 min read

polar-shuffle

  • polar shuffle, bijection based definition
  • polar shuffles form a multicategory
  • polar shuffles form a monoidal multicategory
  • encoding of polar shuffles

Tags: shuffle, partial leaf functions

References.

  • Simple Free Star-Autonomous Categories and Full Coherence (Hughes) serves an inspiration via its notion of partial leaf function.
  • Monoidal Context Theory, PhD Thesis (Roman, 2023) introduces a bijection based version of this definition.

Polar shuffles

Shuffling.

  • shuffling words
  • shuffles are the free physical monoidal multicategory
  • shuffling monoidal category
  • shufflings are deuterorepresentable normal produoidals

Message Theories.

  • naive message theory
  • motivating message theories
  • message passing
  • message theory
  • axioms of a message theory
  • Underlying monoidal of a message structure

Polar Shuffles.

  • polar shuffle
  • polar shuffles form a multicategory
  • polar shuffles form a monoidal multicategory
  • encoding of polar shuffles

Graph View

Backlinks

  • encoding of polar shuffles
  • Message theory
  • polar dependences
  • polar shuffle, bijection based definition
  • Polar shuffles
  • polar shuffles - backtrack counting
  • polar shuffles form a monoidal multicategory
  • polar shuffles form a multicategory
  • shuffle
  • start-of-a-polar-shuffle
  • Monoidal Context Theory, PhD Thesis (Román, 2023)

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