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May. 7th, 2018 09:15 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
timeletsA couple of nights ago I had a bad dream. First, I saw cockroaches crawling around my bed. Most likely they came from a news article I read in the evening about a woman who had a cockroach in her ear for nine days – that cockroach got into her while she was asleep. Naturally, my subconsciousness became concerned about nasty bugs.
Then, the cockroaches climbed into one of my favorite categories and to my horror I saw how they swarmed around pullbacks. I became afraid that my understanding of pullbacks was wrong and the entire theory of transformations I had been advancing was about to fall apart.
There's a reason for that too. Just before going to bed I watched a Milewski lecture on limits and colimits where he covered fibered products. The picture that he drew on the whiteboard surprised me and my brain meshed the two surprises — cockroaches and pullbacks — into a single horror story. The first thing I did the next morning was to check for "bugs" in my CT constructions. Luckily, everything looked ok but, despite the bad dream, I was glad the ever vigilant night brain kept in check the complacent day brain.
Then, the cockroaches climbed into one of my favorite categories and to my horror I saw how they swarmed around pullbacks. I became afraid that my understanding of pullbacks was wrong and the entire theory of transformations I had been advancing was about to fall apart.
There's a reason for that too. Just before going to bed I watched a Milewski lecture on limits and colimits where he covered fibered products. The picture that he drew on the whiteboard surprised me and my brain meshed the two surprises — cockroaches and pullbacks — into a single horror story. The first thing I did the next morning was to check for "bugs" in my CT constructions. Luckily, everything looked ok but, despite the bad dream, I was glad the ever vigilant night brain kept in check the complacent day brain.
