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Jun
23
comment Natural Transformation: Direct Products
Could you provide the reference where this results are stated?
Jun
23
comment Category of sets and multi-valued functions
I think I may understood the difference in this category and the category Rel: it seems that this is due to the fact that the morphism are represented by partial functions instead of ordinary ones. In the definition given above it could happen that a partial function could associates nothing to an element (which is different than associating the empty set to it). Though I'm wondering if that's the only difference between the two categories.
Jun
23
revised Category of sets and multi-valued functions
corrected and equation
Jun
23
comment Category of sets and multi-valued functions
I see, since some authors use dom for source my mistake was understandable (I hope :) ). Anyway I don't understand were the definition of dom is used for the composition.
Jun
23
comment Category of sets and multi-valued functions
Anyway this is not a category composition: a composition need that for every pair of composable morphisms $f$ and $g$ we have that $\text{source}(g \circ f)=\text{source}(f)$, your composition could produce composites where the domain of the composite could be a proper subset of the domain of the first morphism.
Jun
23
comment Category of sets and multi-valued functions
could you provide an example?
Jun
23
answered Category of sets and multi-valued functions
Jun
23
comment Category of sets and multi-valued functions
What's the difference between the category of sets and (binary) relations and the category of sets and multivalued function? They should be the same category, should be?
Jun
23
comment Proving consistency by constructing models? How and why?
@NikolajK that's an interesting question. In my knowledge no one has build an inconsistent set theory after Russell paradox. History tells us that every kind of inconsistency is usually a variation of Russell paradox and is based on self-referentiality: a statement that asserts that is true or false. Since the foundational crisis mathematicians and logicians have learnt to develop systems that do not allow to derive statements of this kind, in this way they builded systems which hopefully should be consistent.
Jun
23
revised Proving consistency by constructing models? How and why?
Improved answer
Jun
23
answered Proving consistency by constructing models? How and why?
Jun
22
comment Does mathematics become circular at the bottom? What is at the bottom of mathematics?
@user119615 I've made edits to the answer, hoping it's more clear now.
Jun
22
revised Does mathematics become circular at the bottom? What is at the bottom of mathematics?
Improved the answer
Jun
22
answered Logic vs. type system
Jun
22
answered Does mathematics become circular at the bottom? What is at the bottom of mathematics?
Jun
20
revised Iterating until a diagram commutes
made a correction in a formula
Jun
20
revised How to introduce type theory to newcomer
improved grammar
Jun
19
answered Iterating until a diagram commutes
Jun
13
awarded  Necromancer
Jun
8
awarded  Yearling