Universality of Coproducts in Categories of Lax Algebras

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• 作者：Mojgan Mahmoudi ; Christoph Schubert and Walter Tholen
• 关键词：Lax (T ; V )(T ; V\ ; ) ; algebra ; universality of coproducts ; extensive category ; topological category
• 刊名：Applied Categorical Structures
• 出版年：2006
• 出版时间：June, 2006
• 年：2006
• 卷：14
• 期：3
• 页码：243-249
• 全文大小：192 KB

文摘

Categories of lax (T,V )(T,V\,)-algebras are shown to have pullback-stable coproducts if TT preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T,V )(T,V\,)-algebras, with TT preserving inverse images. Moreover, we show that any such category of (T,V )(T,V\,)-algebras has a concrete, coproduct preserving functor into the category of topological spaces.