An equational variant of Lawvere's natural numbers object

[摘要] A natural numbers object 1 (0) under right arrow N (S) under right arrow N in a cartesian closed category associates to each pair of arrows a : 1 --> A and h : A --> A a unique arrow f : N --> A such that f0 = a and fS = hf. We call (N, 0, S) a quasi-natural numbers object if the arrow S is unique only up to quasi-equality, where two arrows N --> A are called quasi-equal if they are equalized by the canonical arrow A --> N-(NA). We show that quasi-natural numbers objects can be characterized equationally. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 18C99; 18D99.

[发布日期] 2000-12-01

[效力级别]  Proceedings Paper