منابع مشابه
Final coalgebras in accessible categories
We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p...
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In the field of programming language semantics and concurrency theory, wide attention is paid to the so called name-passing calculi, i.e. formalisms where name generation and passing play a fundamental role. A prototypical example is provided by the π-calculus. The peculiarities of name passing required to refine existing theoretical models and to invent new ones, such as coalgebras over preshe...
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We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.
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We prove that for any Set-endofunctor F the category SetF of F -coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever SetF has finite products.
متن کاملHopf-Algebras and Coalgebras in ∞-Categories
The idea of the following is to suggest an ∞-categorical framework within which the ideas of coalgebras and Hopf-algebras (for various degrees of commutativity and cocommutativity) are natural and easy to define. These foundations will be used to describe interesting examples arising in chromatic homotopy theory and elsewhere in forthcoming work (especially with respect to Thom spectra). Sectio...
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ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2011
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129511000351