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I have constructed products and coproducts, equalizers and coequalizers in my categories Fcd and Rld (continuous maps between endofuncoids and endoreloids). Thus these categories are complete and cocomplete. It is interesting that these (co)limits are presented with algebraic formulas.
Whether they are cartesian closed is yet an open problem. Please help me to solve it.
The above was extracted from my blog
My research (and my book, for now available for free download) is presented at this Web site.
nLab participants, should I further notify you about my progress in applying category theory to my general topology research, or refrain from posting here too much? You also can subscribe to my blog.
The general feeling seems to be this: we’d be glad to update the entry on funcoids/reloids if you prove that the category of endoreloids (or whatever the case may be) is cartesian closed, as this is one benchmark for a category of “spaces” to warrant consideration as being “convenient” (in a technical sense described at convenient category of topological spaces). But otherwise the nLab is not interested in a subscription or piecemeal updates on your research. Individual members may subscribe to your blog if they wish.
Speaking only for myself: at one time I vaguely suggested that the category of endoreloids might form a quasitopos, at least if this category behaves anything like the category of endorelations on sets (which, under the guise of ’user43208’, I indicated was the case in one of my answers to you at Math StackExchange). But at present my difficulty is that I find reloids opaque, and I have no intuition for them or what possible advantage they offer over other frameworks for topology, nor can I see why I should bother learning about them, and so I cannot comment further on this.
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