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In light of my tweet thread about the category of finite sets and commutative monoids (https://t.co/jnY0wZZbxq), I thought I might try to say what the analogue is for braided monoidal things (although much of this is still somewhat hypothetical).
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
So okay, here's a thread on the category of finite sets and a way in which it controls algebraic structure in symmetric monoidal categories. I think it's some really pretty stuff.
— Jonathan Beardsley (@JBeardsleyMath) December 6, 2020
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
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The entire discussion around Facebook’s disclosures of what happened in 2016 is very frustrating. No exec stopped any investigations, but there were a lot of heated discussions about what to publish and when.
In the spring and summer of 2016, as reported by the Times, activity we traced to GRU was reported to the FBI. This was the standard model of interaction companies used for nation-state attacks against likely US targeted.
In the Spring of 2017, after a deep dive into the Fake News phenomena, the security team wanted to publish an update that covered what we had learned. At this point, we didn’t have any advertising content or the big IRA cluster, but we did know about the GRU model.
This report when through dozens of edits as different equities were represented. I did not have any meetings with Sheryl on the paper, but I can’t speak to whether she was in the loop with my higher-ups.
In the end, the difficult question of attribution was settled by us pointing to the DNI report instead of saying Russia or GRU directly. In my pre-briefs with members of Congress, I made it clear that we believed this action was GRU.
The story doesn\u2019t say you were told not to... it says you did so without approval and they tried to obfuscate what you found. Is that true?
— Sarah Frier (@sarahfrier) November 15, 2018
In the spring and summer of 2016, as reported by the Times, activity we traced to GRU was reported to the FBI. This was the standard model of interaction companies used for nation-state attacks against likely US targeted.
In the Spring of 2017, after a deep dive into the Fake News phenomena, the security team wanted to publish an update that covered what we had learned. At this point, we didn’t have any advertising content or the big IRA cluster, but we did know about the GRU model.
This report when through dozens of edits as different equities were represented. I did not have any meetings with Sheryl on the paper, but I can’t speak to whether she was in the loop with my higher-ups.
In the end, the difficult question of attribution was settled by us pointing to the DNI report instead of saying Russia or GRU directly. In my pre-briefs with members of Congress, I made it clear that we believed this action was GRU.
