Journal article
When ∏ is Isomorphic to
Communications in algebra, Vol.34(12), pp.4551-4562
12/01/2006
DOI: 10.1080/00927870600936674
Abstract
For a category , we investigate the problem of when the coproduct ⊕ and the product functor ∏ from
I
to are isomorphic for a fixed set I, or, equivalently, when the two functors are Frobenius functors. We show that for an
Ab
category this happens if and only if the set I is finite (and even in a much general case, if there is a morphism in that is invertible with respect to addition). However, we show that ⊕ and ∏ are always isomorphic on a suitable subcategory of
I
which is isomorphic to
I
but is not a full subcategory. If is only a preadditive category, then we give an example that shows that the two functors can be isomorphic for infinite sets I. For the module category case, we provide a different proof to display an interesting connection to the notion of Frobenius corings.
Details
- Title: Subtitle
- When ∏ is Isomorphic to
- Creators
- Miodrag Cristian Iovanov - University of Bucharest
- Resource Type
- Journal article
- Publication Details
- Communications in algebra, Vol.34(12), pp.4551-4562
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/00927870600936674
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 12/01/2006
- Academic Unit
- Mathematics
- Record Identifier
- 9984241155402771
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