A Functor from Formless Ideas to Verbose Paragraphs
Welcome to the category of algebras for my “free thinking” monad! It is (by design) a bit lacking in structure, being neither complete nor cocomplete.
On the bright side, this means there are few limits to what can be found here (and likewise for colimits)! By the dichotomy between “nice” objects and “nice” categories, perhaps this also means that the content you find here will be of better quality?
That being said, there isn’t no structure: my posts are organised into five subcategories (see here for a description). If you’re new here, (welcome!) check out my “3 levels” posts! Each post is divided into three sections (over lunch, on the bus, in the lounge) which organise the discussion in increasing difficulty from general audience to graduate maths student.
When a subject like group theory is presented to the general public, the examples used (e.g., symmetries of shapes) always seem to give this impression that group theory is a “fun toy” mathematicians play with, rather than something actually quite serious and useful.
Continuing off the tangent from the last story, it’s important to make sure you keep yourself oriented so that you can track how far off-topic you take yourself with your thoughts.
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If you’re more mathematically inclined (i.e., you can read the “In the lounge” sections of my 3 Levels posts), then you may also be interested in my other posts:
What is the “infinite”th (?) term of the following sequence: a, b, a, b, a, b, …? Would it be “a” or “b”? How about the “infinite”th term of the sequence a, a, a, a, a, a, …? Would it be “a”?
The category of sets is complete precisely because it is the prototypical source of examples of limits. How does this have anything to do with colimits of sets?
Don’t get too excited about the word “super” in mathematics. Perhaps you also shouldn’t get too excited by this blog’s title. Imagine if Superman were just a man with a Z/2-grading.
Left Adjoint to Forgetful Thinking 