Tag Archives: category theory

Exponentiable locales I: every exponentiable locale is continuous

The exponentiable objects of Top are exactly the core-compact spaces. Through Stone duality, the core-compact spaces are related to the continuous frames. So here is a wild guess: would the exponentiable locales be exactly the continuous frames? That is indeed … Continue reading

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Topological Functors II: the Cartesian-closed category of C-maps

Some time ago, I gave an introduction to topological functors. They form a pretty brilliant categorical generalization of topological spaces. The point of today’s post is to give one particular example of the fact that you can somehow generalize some … Continue reading

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Topological functors I: definition, duality, limits and colimits

I have briefly mentioned topological functors in a recent post. It is time for me to explain what they are. This is a truly wonderful concept, which abstracts topological spaces away and concentrates on the key properties of the forgetful … Continue reading

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