Topology from the Perspective of Category Theory

Re:Topology from the Perspective of Category Theory by openfuture on Thursday September 10, 2020 @04:06AM (#24430004)

The requirement for finiteness means you are just working with lattices. Topology approached via frame homomorphisms (like in the nlab book) makes this clear.

Disclaimer: not a mathematician (yet)

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Re:Topology from the Perspective of Category Theory by taliesinb on Thursday September 10, 2020 @06:25AM (#24430840)

Thanks! By nlab book you mean the whole nlab project? Also, can you help me understand the connection to lattices? Do they model intersection and union of open sets? Why is finiteness needed for lattices to be appropriate?

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Re:Topology from the Perspective of Category Theory by openfuture on Thursday September 10, 2020 @02:34PM (#24435196)

I meant [1] they use frames [2] to explain what a topology is but in a finite setting the frame becomes a lattice because you only have finite meets and joins.

[1]: https://ncatlab.org/nlab/show/Introduction+to+Topology [2]: https://ncatlab.org/nlab/show/frame

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