Question
These structures are the objects in the representative example of a compact closed category. Modules are analogs to these structures defined over rings, and an algebra equips one of these structures with a bilinear product on a field. A representation is a group homomorphism from a group G to the automorphism group of one of these structures. The set of linear functionals on one of these structures forms [emphasize] another one of these structures called the (*) dual space. Norms assign elements of these structures to non-negative reals and may be induced by an inner product. Linear maps are functions between these structures, which are closed under addition and scalar multiplication. The number of elements of the basis of one of these structures gives their dimension. For 10 points, identify these sets consisting of objects that may have a magnitude and direction. ■END■
Summary
2023 ARCADIA at Duke | Emory, Duke, Yale | Y | 4 | 75% | 0% | 25% | 132.67 |
2023 ARCADIA at Emory | Emory, Duke, Yale | Y | 4 | 75% | 25% | 50% | 101.00 |
2023 ARCADIA at Imperial | Imperial | N | 5 | 80% | 60% | 20% | 48.00 |
2023 ARCADIA Online | Maryland, Online | N | 3 | 100% | 33% | 0% | 60.00 |
2023 ARCADIA at Maryland | Maryland, Online | N | 3 | 67% | 33% | 0% | 50.00 |
2023 ARCADIA at Ohio State | Ohio State, Texas | Y | 3 | 67% | 0% | 33% | 93.00 |
2023 ARCADIA at Texas | Ohio State, Texas | Y | 3 | 67% | 33% | 0% | 73.00 |
2023 ARCADIA at WUSTL | Premiere | N | 3 | 67% | 0% | 33% | 137.50 |
2023 ARCADIA at UC Berkeley | Premiere | N | 2 | 100% | 100% | 0% | 20.50 |
2023 ARCADIA at Carleton University | Premiere | N | 3 | 67% | 33% | 33% | 48.00 |
2023 ARCADIA at Claremont Colleges | Premiere | N | 1 | 100% | 100% | 0% | 26.00 |
2023 ARCADIA at Indiana | Premiere | N | 5 | 80% | 20% | 80% | 97.50 |
2023 ARCADIA at RIT | Premiere | N | 2 | 100% | 50% | 0% | 69.00 |
Buzzes
Player | Team | Opponent | Buzz Position | Value |
---|---|---|---|---|
Arya Karthik | Georgia Tech D | Georgia Tech A | 21 | 15 |
Chinmay Murthy | Texas A | Texas B | 22 | 15 |
Rohan Dalal | Georgia Tech C | Georgia Tech B | 56 | -5 |
Dennis Yang | Michigan B | Ohio State B | 77 | 10 |
James Stevenson | Michigan A | Kenyon A | 94 | -5 |
Jon Golan | Georgia A | Tennessee A | 109 | -5 |
Calvin | OSU A | Kenyon B | 109 | 10 |
John Nolan | NC State | James Madison A | 121 | 10 |
Jack Oberman | South Carolina A | North Carolina A | 121 | -5 |
Dimitris Kalafatis | TAMU | HCC | 124 | 10 |
Ivan Stanisavljevic | Duke | James Madison B | 136 | 10 |
Benjamin McAvoy-Bickford | North Carolina B | South Carolina B | 141 | 10 |
Benny Shtutman | South Carolina B | North Carolina B | 141 | 0 |
Martin Brandenburg | Georgia B | Emory A | 141 | 10 |
Alexander Wyrick | Tennessee A | Georgia A | 141 | 0 |
Tarun Koti | Emory A | Georgia B | 141 | 0 |
Quentin Mot | Georgia Tech B | Georgia Tech C | 141 | 10 |
Owen Brown | Kenyon A | Michigan A | 141 | 0 |
Ketan Pamurthy | TAG Magnet: Taylor's Version | Texas C | 141 | 0 |
Gia Harvey-Slager | Texas C | TAG Magnet: Taylor's Version | 141 | 0 |