Mathematical Conceptware: Category Theory: RALF KROMER. Tool and Object: A History and Philosophy of Category Theory
Bibliographic record
Abstract
Category theory has been used by mathematicians for more than sixty years now. Its importance in algebraic geometry, algebraic topology, and homological algebra is indisputable. Its overall significance in mathematics and the foundations of mathematics is still a matter of debate. An historical analysis of the origins and development of category theory (CT) might shed an interesting light on various issues related to this significance. Ralf Krömer’s book constitutes the first global attempt at such an analysis. It is based on extensive original sources, and it offers an original and challenging perspective. It definitely should be read by historians and philosophers of contemporary mathematics. The book’s main thesis is that a form of pragmatism best describes the implicit philosophy of mathematicians using and developing CT from 1945 to approximately 1970. The thesis is primarily defended by looking at the history of CT, and the latter is organized by following the interactions of CT with three fields: algebraic topology, homological algebra, and algebraic geometry. This does indeed roughly follow the actual development of the field and is thus entirely justified.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.011 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".