Question
William Lawvere was inspired by Hegelian dialectics to promote this subfield as the basis of mathematical foundations. For 10 points each:
[10e] Name this subfield of mathematics often derided as “abstract nonsense.” Mac Lane and Eilenberg used the philosophical term “functor” for maps between this field’s namesake collections of objects and morphisms.
ANSWER: category theory [accept categories]
[10h] Two answers required. Lawvere borrowed the dialectical idea of “unity of opposites” to name functors with adjoints that satisfy these two properties. Functors with these two properties induce bijections between hom-sets in their source and target.
ANSWER: full AND faithful [or fully faithful]
[10m] Lawvere’s “Hegelian taco” is a display of the “graphic” type of these algebraic structures. Because they are equipped with an associative operation and an identity element, these structures may be viewed as single-object categories.
ANSWER: monoid [or monoidal category; accept graphic monoid; reject “monad”]
<AK, Other Science (Math)>
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| There are buzzable clues everywhere for those with eyes to see | BHSU B | 10 | 0 | 10 | 20 |
| sticking out your guyot for the ridge push; you're so seafloor spread, you're so fracture zone | The Dyatlov Passement incident | 10 | 0 | 10 | 20 |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2024 Chicago Open | 07/28/2024 | Y | 2 | 20.00 | 100% | 100% | 0% |