Abstract
We prove a pushout theorem for localizations and Kleisli categories over a symmetric monoidal closed categoryV. That is, suppose ∑ is aV-localizable subcategory of aV-categoryA and thatT=(T,η,μ) is aV-monad onA. Then under suitable relations betweenT and ∑ we show that there is aV-monadT′ induced onA[∑-1] such that the Kleisli category ofT′ is the pushout of the localization functor Φ:A→A[∑-1] and the free functor F:A→K(T). Consequently,K(T′)≈K(T) [S-1] for some S ⊑K(T). We give several examples of this situation.
Keywords
Number Theory Algebraic Geometry Topological Group Localization Functor Suitable Relation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [1]ALMKVIST, G.: Fractional categories. Arkiv for Math.7, 449–476 (1969).Google Scholar
- [2]BUNGE, M.: Relative functor categories and categories of algebras. J. of Algebra.11, 64–101 (1969).Google Scholar
- [3]DUBUC, E.: Kan extensions in enriched category theory. Lecture Notes in Mathematics144, Springer-Verlag 1970.Google Scholar
- [4]EILENBERG, S. and KELLY, G.M.: Closed categories. Proceedings of the Conference on Categorical Algebra, Springer-Verlag, 1966.Google Scholar
- [5]GABRIEL, P. and OBERST, U.: Spektralkategorien und regulare Ringe in Von-Neumannschen Sinn. Math. Z.92, 389–395 (1966).Google Scholar
- [6]GABRIEL, P. and ZISMAN, M.: Calculus of Fractions and Homotopy Theory. Springer-Verlag 1967.Google Scholar
- [7]HARTSHONE, R.: Residues and duality. Lecture Notes in Mathematics20, Springer-Verlag, 1966.Google Scholar
- [8]KOCK, A.: Monads on symmetric monoidal closed categories. Arch. Math.21, 1–10 (1970).Google Scholar
- [9]KOCK, A.: Closed categories generated by commutative monads. J. of the Australian Math. Soc., XII, 405–424 (1971).Google Scholar
- [10]MEYER, J.P.: Induced functors on categories of algebras. Preprint.Google Scholar
- [11]MITCHELL, B.: Theory of Categories. Academic Press 1965.Google Scholar
- [12]QUILLEN, D.G.: Rational homotopy theory. Annals of Math.90, 205–295 (1969).Google Scholar
- [13]STREET, R.: The formal theory of monads. J. of Pure and Applied Algebra2, 149–168 (1972).Google Scholar
- [14]
Copyright information
© Springer-Verlag 1975