On universal categories of coalgebras
✍ Scribed by Věra Trnková; Jiří Sichler
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 296 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0002-5240
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For any Set-endofunctor F, the category SetF of F-coalgebras has preimages, i.e. pullbacks along an injective map. If F preserves preimages, then SetF is distributive, and the converse holds, whenever SetF has ÿnite products.
We will freely use ''sigma notation'': ⌬ c s Ý c m c for the comulti-1 2 Ž . plication of a coalgebra C and m s Ý m m m for the structure map 0 1 of a right C-comodule M. Ž . For any abelian category A A we denote Z A A its centre, i.e., the commutative ring of all natural morphisms of the identity
In this article we deÿned and studied quasi-ÿnite comodules, the cohom functors for coalgebras over rings. Linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing but a cotensor functor. Our main result of this work characte