In Chapter IX, Sec 6, Ex 3 of CWM, MacLane defines the twisted arrow category of C such that objects are arrows f : a -> b of C and arrows are pairs of morphisms of C, (l,m) : f -> g, such that g = mfl. The construction is part of a proof of the reduction of ends to limits. I would be grateful for pointers to other occurrences of this construction in the literature. Lindsay Errington
In Chapter IX, Sec 6, Ex 3 of CWM, MacLane defines the twisted arrow category of C such that objects are arrows f : a -> b of C and arrows are pairs of morphisms of C, (l,m) : f -> g, such that g = mfl. The construction is part of a proof of the reduction of ends to limits.
I would be grateful for pointers to other occurrences of this construction in the literature.
The twisted arrow category of A is the category of elements of the hom functor A(-,-) : A^op x A --> Set. In internal and variable category theory there is a sense in which the twisted arrow fibration comes first and then can be used to define hom functors and local smallness. For example, see page 292 of my paper Cosmoi of internal categories, Transactions American Math. Soc. 258 (1980) 271-318; MR82a:18007 Regards, Ross www.mpce.mq.edu.au/~street/
The twisted arrow category is discussed in my paper "Extension Theories for Categories", available at http://www.cwru.edu/artsci/math/wells/pub/papers.html (it has never been published).
In Chapter IX, Sec 6, Ex 3 of CWM, MacLane defines the twisted arrow category of C such that objects are arrows f : a -> b of C and arrows are pairs of morphisms of C, (l,m) : f -> g, such that g = mfl. The construction is part of a proof of the reduction of ends to limits.
I would be grateful for pointers to other occurrences of this construction in the literature.
Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html
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Charles Wells -
Lindsay Errington -
street＠mpce.mq.edu.au