Mario Román

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profunctor

profunctor

Jul 24, 20251 min read

profunctor

Profunctors.

  • composing profunctors
  • profunctor natural transformation

Profunctors form a bicategory: hom is the identity profunctor, and profunctor composition is associative.

Promonads.

  • motivation for promonads
  • promonad, a monoid in the bicategory of profunctors
  • promonad homomorphism, or natural transformation
  • Kleisli category of a promonad
  • Promonads are id-on-objects functors
  • Central product of promonads
  • Pure tensor of promonads
  • Funny tensor of promonads
  • distributive law of promonads
  • distributive law of strong promonads
  • promodule

Promonoidal categories.

  • promonoidal category
  • promonoidal functor

Strong profunctors, with a bit of promonoidals.

  • Strong profunctor
  • Bimodular profunctor
  • pro or not, strong or not
  • Strong monad
  • Strong promonad
  • Prostrong monad
  • Prostrong promonad

Monoidal profunctors.

  • monoidal profunctor
  • monoidal promonad
  • Map pseudomonoid
  • Lax twisted arrow bicategory
  • Mates correspondence
  • Convolution and coconvolution
  • Duoidal Tambara
  • produoidal normalization
  • Raudsilla Seminar, November 2022

Monoidal bicategory of profunctors.

  • monoidal bicategory of profunctors
  • Reading an example on the monoidal bicategory of profunctors
  • Open diagram
  • open diagrams are pointed profunctors

Profunctors with structure.

  • multivariable adjunction
  • Pointed profunctor
  • Lack coherence theorem
  • Composition along a channel
  • Reversors in profunctors

Tags: category theory.


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Backlinks

  • Index
  • Composition along a channel
  • Reading an example on the monoidal bicategory of profunctors
  • Reversors in profunctors
  • category theory
  • Components of the monoidal bicategory of profunctors
  • composing profunctors
  • hom is the identity profunctor
  • Multivariable adjunction
  • Open diagrams are pointed profunctors
  • promodule
  • promonad natural transformation
  • promonoidal category
  • representable profunctor
  • Monoidal Context Theory, PhD Thesis (Román, 2023)
  • Open Diagrams via Coend Calculus (Román, 2020)

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