Paul Taylor
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 2d comment “Downward closed” relation on a poset Relations for which $x'\leq x R y\leq y'\Longrightarrow x' R y'$ are most certainly a very common kind of animal. Mappings $X\to T X$ for any endofunctor of any category are another very common kind of animal, called a coalgebra, which enough people study to run a conference series. Apr 25 comment Probability theory without deductive closure Excellent question and cursed be those that say otherwise. Apr 24 comment origin of analogy “primes as the atoms of number theory/ arithmetic” People have talked about "atoms" in Boolean algebras since long before 1968, as I am sure Paul Cohn knew. This question is related to mine and it would be nice if they got a serious answer from a historian. Apr 24 comment Small object argument for multiple factorization systems @FoscoLoregian Forget "smallness" and "transfinite" - they are part of the superstition of set theory. The notion of a factorisation system on a category is finitary and you need finitary structure such as pullbacks to make it work. If you're interested in multiple factorisation systems on a category then why not start with the problem that I gave you, namely finding out whether they form a modular or distributive lattice. Apr 24 revised Small object argument for multiple factorization systems corrected link to book Apr 24 answered Small object argument for multiple factorization systems Apr 24 comment Small object argument for multiple factorization systems What is the "small object argument"? What is the problem that you are trying to solve? Apr 22 comment Are product / coproduct projections / inclusions 'semistrict'? Presumably this is a standard result for Abelian categories, so you should examine the textbook proof to see if it generalises. It seems unlikely to me, because, in the absence of subtraction, the kernel of $f$ should be $\{(x,y)|f(x)=f(y)\}$ not just $\{x|f(x)=0\}$ as presumably you're using. Zurab Janelidze did some work on generalising Abelian categories that might be relevant. Apr 22 revised Factorization system “tilted” by $(L,R)$ added 395 characters in body Apr 22 revised Factorization system “tilted” by $(L,R)$ added 46 characters in body Apr 21 comment Are product / coproduct projections / inclusions 'semistrict'? What are pseudomonomorphisms and pseudoepimorphisms? Apr 21 revised Factorization system “tilted” by $(L,R)$ added 71 characters in body Apr 21 revised Factorization system “tilted” by $(L,R)$ deleted 15 characters in body Apr 21 revised Factorization system “tilted” by $(L,R)$ added 11 characters in body Apr 21 answered Factorization system “tilted” by $(L,R)$ Apr 21 comment Factorization system “tilted” by $(L,R)$ In what application does this arise? Apr 20 comment Difference between constructive Dedekind and Cauchy reals in computation @ValerySaharov You already have several good answers to your math.stackexchange question from people who are better qualified than me, whilst I am not subscribed. "Completed infinite calculation" doesn't relate to "real calculation" at all - it is an idealisation by "constructive mathematics". Apr 20 comment Difference between constructive Dedekind and Cauchy reals in computation @ValerySaharov "If I do (correct) calculations I expect the algorithms to meet specific requirements." But there may be different results (steps and sequences) that both meet the requirements. In the example of representing real numbers by Cauchy sequences this is necessarily the case, for topological reasons. It is natural from the point of view of an ongoing calculation. ACC is needed if you consider the completed infinite calculation, turning a succession of choices of steps into a single choice of a sequence. Apr 19 revised Difference between constructive Dedekind and Cauchy reals in computation changed title Apr 19 revised Difference between constructive Dedekind and Cauchy reals in computation completely rewritten