# Totally distributive toposes

@article{LucyshynWright2012TotallyDT, title={Totally distributive toposes}, author={R. B. Lucyshyn-Wright}, journal={Journal of Pure and Applied Algebra}, year={2012}, volume={216}, pages={2425-2431} }

Abstract A locally small category E is totally distributive (as defined by Rosebrugh and Wood) if there exists a string of adjoint functors t ⊣ c ⊣ y , where y : E → E is the Yoneda embedding. Saying that E is lex totally distributive if, moreover, the left adjoint t preserves finite limits, we show that the lex totally distributive categories with a small set of generators are exactly the injective Grothendieck toposes , studied by Johnstone and Joyal. We characterize the totally distributive… CONTINUE READING

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