Universality of Coproducts in Categories of Lax Algebras |
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Authors: | Mojgan Mahmoudi Christoph Schubert Walter Tholen |
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Institution: | 1. Department of Mathematics, Shahid Beheshti University, Tehran, 19839, Iran 2. Software-Technology, Fachbereich Informatik, Universit?t Dortmund, 44221, Dortmund, Germany 3. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada
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Abstract: | Categories of lax -algebras are shown to have pullback-stable coproducts if 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 -algebras, with preserving inverse images. Moreover, we show that any such category of -algebras has a concrete, coproduct preserving functor into the category of topological spaces. |
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Keywords: | Lax gif" alt="$(T V\ -algebra" target="_blank">)$" align="middle" border="0">-algebra universality of coproducts extensive category topological category |
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