Black & white portraits of Lilly from a summer day in the garden.


#blackandwhite #portrait #femaleportrait #hamburg #hamburgphotographer #fotografie #photography #braided

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Braided Seal Gut β€” Qiluryaq
Taugkut qiluryat ekllinartut. – Those braided seal gut look delicious.

Visitors to Kodiak often ask how Alutiiq people can hunt protected species like sea otters and sea lions. In 1972, the Marine Mammal Protection Act prohibited the harvesting of all marine mammals to preserve their populations. However, this law recognizes the importance of sea...
https://alaska-native-news.com/75706-2/75706/
#braided-seal-gut #alutiiq #Wordoftheweek #museum

- Alaska Native News

Braided Seal Gut β€” Qiluryaq Taugkut qiluryat ekllinartut. – Those braided seal gut look delicious. Visitors to Kodiak often ask how Alutiiq people can hunt protected species like sea otters and sea lions. In 1972, the Marine Mammal Protection Act prohibited the harvesting of all marine mammals to preserve their populations. However, this law recognizes […]

Alaska Native News
Thomsen River Estuary, Banks Island

Sea ice and waterways along the north side of Canada’s high-Arctic island reveal compelling patterns when viewed from above.

New paper πŸŽ‰πŸŽ‰
About coherence πŸ₯±πŸ’€β‰οΈ

joint work with Nick Gurski
https://arxiv.org/abs/2312.11261

The title is:
Universal pseudomorphisms, [*deep breath*]
with applications to diagrammatic coherence for braided and symmetric monoidal functors πŸ™ƒπŸ˜Έ

I've always thought coherence theorems sound boring, but actually they're good! In this paper we take a problem that is hard (coherence for structured functors), do a *bunch* of really abstract stuff (2-monad theory), and come out with a solution that makes your life* significantly better.

[*Here, "your life" means the part of your life you spend checking diagrams of braided monoidal functors. Or, more generally, pseudomorphisms for algebras over a 2-monad.]

Almost 1/5 of this paper is dedicated to real, genuine examples, and that's what I want to focus on below. I'll say just a bit about the more abstract machinery on which the examples are based. If you've been following along, this is the culmination of my series "weird facts about monoidal functors and coherence" [1,2,3,4].

[1] https://mathstodon.xyz/@nilesjohnson/110741323263984146
[2] https://mathstodon.xyz/@nilesjohnson/110876487813747736
[3] https://mathstodon.xyz/@nilesjohnson/110979458364785667
[4] https://mathstodon.xyz/@nilesjohnson/111070640771166081

#CategoryTheory #MonoidalFunctor #Coherence #Braided #Symmetric #PseudomorphismClassifier

(1/14)

Universal pseudomorphisms, with applications to diagrammatic coherence for braided and symmetric monoidal functors

This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of strict algebras. Applications include diagrammatic coherence for plain, symmetric, and braided monoidal functors. The final sections include a variety of examples.

arXiv.org

Killing these baby darlings too
#braided bronze or #glassjewellery

* * *

Dags att ha ihjΓ€l de hΓ€r Γ€lsklingarna ocksΓ₯
#flΓ€tat #brons eller #glassmycken

Pazifica #braided my #hair again. In #waterfallStyle this time πŸ₯°

#GalentinesWeek continues.

#hairstyles #friendship

- A #braided #monoidal category is called symmetric if { \gamma } also satisfies {gamms _{B,A}\circ \gamma _{A,B}=Id} for all pairs of objects { A, B}. In this case action of { \gamma } on an { N}-fold tensor product factors through the symmetric group