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Dec
9
comment Uniqueness of the long exact sequence in homology
I doubt you could get away with that. Actually, I doubt you could avoid looking at the construction of spectral sequences. (The "proof" with spectral sequences is almost surely circular. You need the long exact sequence in homology in order to construct the spectral sequence of a filtered complex.)
Dec
8
comment About certain regular epimorphisms in a Grothendieck Topos
In fact, if you can prove it for $\mathbf{Set}$, then it holds in any Grothendieck topos, because your question only involves finite limits and colimits. Also, every epimorphism is already regular.
Dec
8
awarded  Caucus
Dec
7
revised Proving distributivity of Heyting algebras with the Yoneda lemma.
edited tags
Dec
7
comment How to use bijection of two sets to define a bijection of their respective differences?
No. For instance, let $B$ be a countably infinite proper subset of a countably infinite set $A$.
Dec
7
comment Category with pullbacks but not equalizers
At a guess, I would say $\mathbf{LH}$, the category of topological spaces and local homeomorphisms.
Dec
7
comment Intersection of localizations of an integral domain
Well, $A \subseteq \bigcap_\mathfrak{p} A_\mathfrak{p} \subseteq \bigcap_\mathfrak{m} A_\mathfrak{m}$, so if $\bigcap_\mathfrak{m} A_\mathfrak{m} = A$ then certainly $\bigcap_\mathfrak{p} A_\mathfrak{p} = A$. This is just elementary set theory.
Dec
7
revised Model structure on sSet
added 333 characters in body
Dec
7
comment Does an interpretation of a structure by itself induce a bijection on the automorphism group of the structure?
Yes, but if you read the part where he actually defines the functor he talks about signatures.
Dec
7
comment Does an interpretation of a structure by itself induce a bijection on the automorphism group of the structure?
Your terminology is not entirely precise. One does not have an interpretation of one structure in another but rather of one signature in another, subject to conditions etc.
Dec
6
comment What does $S^z$ mean for each $z\in\mathbb{C}$?
Frankly, no, none of this makes any sense. Not everything is begging to be generalised.
Dec
6
comment No injection $Ord \to A$
So you are being asked to construct the Hartogs number?
Dec
6
comment Colimits in full subcategory (of all monics) of arrow category
Not really. Just read category theory in general, I suppose.
Dec
6
comment Catsters Video Question
Of course adjunctions have a direction (but it is a matter of convention as to what that direction is). Anyway, $1$ means identity. (I avoid this notation.)
Dec
6
comment About mapping cone complex
Yes. The mapping cone induces a long exact sequence and you can use the five lemma. There are some details in the introduction of Weibel's book on homological algebra.
Dec
6
revised Model structure on sSet
deleted 17 characters in body
Dec
5
comment About mapping cone complex
The mapping cone of chain complexes is something that can be defined purely algebraically. It is analogous to the mapping cone of spaces but there is no reason to define one in terms of the other.
Dec
5
awarded  Revival
Dec
4
revised Model structure on sSet
edited tags
Dec
4
answered Model structure on sSet