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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 $(L,R)$
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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 $(L,R)$
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Apr
21
revised Factorization system “tilted” by $(L,R)$
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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