Core varieties, extensivity, and rig geometry.
Lawvere, F.William (2008)
Theory and Applications of Categories [electronic only]
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Lawvere, F.William (2008)
Theory and Applications of Categories [electronic only]
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Kučera, L., Pultr, A.
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Jiří Rosický (1982)
Archivum Mathematicum
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Jan Jastrzębski (1983)
Fundamenta Mathematicae
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Julia E. Bergner, Philip Hackney (2015)
Fundamenta Mathematicae
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We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new...
Roman Pol (1979)
Fundamenta Mathematicae
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Diers, Yves (2005)
Theory and Applications of Categories [electronic only]
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Federico De Marchi, Neil Ghani, Christoph Lüth (2003)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely...
Artem Anisimov (2012)
Colloquium Mathematicae
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Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible...