- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 30
- On Adjointness of Comma Categories
On Adjointness of Comma Categories
Authors : M. Irfan
Pages : 0-0
Doi:10.1501/Commua1_0000000104
View : 5 | Download : 4
Publication Date : 1981-01-01
Article Type : Research
Abstract :In this paper we determine a SUMMARY pair of adjoint functors for the categories (T । A) and and (T' । A') where T and T' are functors from to Q and A and A' are objects of A precise dcfinition of a Comma Category (T | A) where T is a functor from a category "g to another category Q and A is an obiect of g, in the sense of Maclane [2 ], can be stated as: The objects of (T | A) are pairs (B, b) with B h: (B,b) 1^1 andb:TB A and the morphisms (B', b') are those morphisms h: B -> B' in^ for ■which b'o Th = b. In the present note we determine a pair of adjoint functors for the categories (T | A) and (T' | A') where, again. T' is a functor from "S to Q and A' is an object of g. Lemma 1: If a: T'-> T' is a natural transformation and u: A A' is a morphism, then for (B, b) in (T | A) the rule (B, b) defines a functor K: (T A) Proof: If we define R on (T' I A') morphisms as: for any f: (B, b) (B, ub a B) (B', b') e R (f) = f such that ub'aB'oT' f = ub aB; that is, the following diagram commutesKeywords : Adjointness, Comma Categories, Statistics