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Nov
29
comment Exact sequence in a category with zero morphisms
It doesn't seem to be on SpringerLink, for some reason. I suppose it might be available elsewhere.
Nov
29
comment Exact sequence in a category with zero morphisms
I added the quote.
Nov
29
revised Exact sequence in a category with zero morphisms
added 263 characters in body
Nov
29
comment Lawvere theories: an equivalence.
The category $\mathcal{C}$ is a Lawvere theory, if you have a bijective-on-objects product-preserving functor $\mathbb{N}^\mathrm{op} \to \mathcal{C}$.
Nov
29
comment Intuitive Understanding of Projective Modules
Every projective module is indeed locally free, but the converse requires some hypotheses: see here.
Nov
29
comment Intuitive Understanding of Projective Modules
A projective module is the next best thing to a free module.
Nov
29
revised Every projective f. g. module is f. p.
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Nov
29
answered Exact sequence in a category with zero morphisms
Nov
28
comment Why $F^{+}$ is a monopresheaf?
Well, you can see $F^+$ as a subpresheaf $F^{++}$, which is the sheaf of sections of the associated espace étalé.
Nov
28
comment Can functor carry over a monoidal structure?
Again with dogma! There is a time and place for everything: even equality of objects. And strict monoidal categories are perfectly definable if you believe there is a 2-category of categories. And the 2-monad it induces is precisely the one for which (unbiased) monoidal categories are pseudoalgebras. One may then use 2-monad theory to deduce the coherence theorem. So I dare you to say that strict monoidal categories are not useful.
Nov
28
comment Why $F^{+}$ is a monopresheaf?
There is no hope of interpreting $(-)^+$ in terms of espace étalé, because those things are already sheaves...
Nov
28
revised Why $F^{+}$ is a monopresheaf?
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Nov
28
comment What is a (the?) good starting point for learning the modern “higher” mathematics?
Topos theory is not scary in the least, especially not compared to the higher abstract nonsense you are talking about. But it seems to me you are worried about sinking into generalities – so first you must answer the question, what is it you really want to do?
Nov
28
revised What is a (the?) good starting point for learning the modern “higher” mathematics?
edited tags
Nov
27
comment Why is the unit of a compact closed category coordinate-independent?
It corresponds to ($r$ times) the identity matrix. Isn't that obviously coordinate independent?
Nov
27
comment Can functor carry over a monoidal structure?
Yet, it is not true that a category equivalent to a strict monoidal category is again a strict monoidal category. So there is something slightly non-trivial going on...
Nov
27
comment Can functor carry over a monoidal structure?
Yes. There is a nice abstract nonsense way of seeing this using pseudoalgebras for a 2-monad.
Nov
27
comment What are some practical applications of mathematical/formal logic to science and humanities?
This calls to mind a remark of Vaughan Pratt: "It has been my impression from having dealt with a lot of lawyers over the last twenty years that the logic of the legal profession is rarely Boolean, with a few isolated exceptions such as jury verdicts which permit only guilty or not guilty, no middle verdict allowed. Often legal logic is not even intuitionistic, with conjunction failing commutativity and sometimes even idempotence. But that aside, excluded middle and double negation are the exception rather than the rule."
Nov
26
comment Deeper studies in Category Theory: suggestions and references.
Plenty! There's an equally vast branch of categorical algebra (i.e. category-theoretic abstract algebra), after all...
Nov
26
revised Properties of the internal language of the category of sheaves.
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