Reducible 2-categories. (2-catégories réductibles. (Originally published as preprint, January 1978).) (French. English summary) Zbl 1234.18004
This is a publication of the preprint from 1978. This publication seems to be even more appropriate in view of the recent surge of activity related to structures based on \(2\)-categories (“higher-dimensional algebra”, etc.)
From the summary: “It is well known that in the category of sets, pulling back a map \(f: X \to Y\) along itself produces an equivalence relation on the set \(X\) which determines a bijection between the equivalence relations on \(X\) and the surjections with domain \(X\).”
This paper is devoted to investigation of \(2\)-categories where a similar phenomenon holds, with pullback being replaced by the “comma” construction of the function \(f\) with itself, and related questions.
From the summary: “It is well known that in the category of sets, pulling back a map \(f: X \to Y\) along itself produces an equivalence relation on the set \(X\) which determines a bijection between the equivalence relations on \(X\) and the surjections with domain \(X\).”
This paper is devoted to investigation of \(2\)-categories where a similar phenomenon holds, with pullback being replaced by the “comma” construction of the function \(f\) with itself, and related questions.
Reviewer: Pasha Zusmanovich (Tallinn)
MSC:
| 18D05 | Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) |
| 18A32 | Factorization systems, substructures, quotient structures, congruences, amalgams |
| 18B25 | Topoi |
| 18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
| 18D35 | Structured objects in a category (MSC2010) |
