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Nov
29
comment Is there a special name or any research on Cartesian compact closed categories?
The category of finite dimensional vector spaces is a compact closed category and has finite products.
Nov
29
answered Example of endofunctor in Cat that is not a 2-functor.
Nov
29
revised an example of the Scott topology
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Nov
28
comment Set and category theory
Your two questions are very different and should be asked separately. Some brief comments: (1) You should specify the axioms of set theory you are considering. (2) The vector space structure on an affine space is not natural.
Nov
28
comment Are varieties cocomplete?
You should ask your question about injective objects/cogenerators separately.
Nov
28
answered Are varieties cocomplete?
Nov
28
answered Is there a special name or any research on Cartesian compact closed categories?
Nov
28
comment What exactly is Standard Coordinates?
"Standard" is being used as an ordinary English word here.
Nov
28
comment Can every basic concept of fundamental group be generalized to homotopy group?
I don't agree. For one thing, the higher homotopy groups are all abelian, but $\pi_1$ is not necesarily abelian (and $\pi_0$ is not even a group). For another, there's the beautiful connection between $\pi_1$ and covering space theory...
Nov
27
comment Uniqueness of the long exact sequence in homology
The connecting morphism is not quite unique. You could replace $\delta_n$ with $-\delta_n$, for example. So there is a genuine ambiguity. Regardless, the long exact sequence (including the connecting morphism) can be defined in a very natural way one you have the notion of mapping cone.
Nov
27
revised Uniqueness of the long exact sequence in homology
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Nov
27
comment Functorial cofibrant replacement does not have to be fibration?
Well, if you are only interested in showing that morphisms in $\operatorname{Ho} \mathcal{M}$ (defined by its universal property) can be factored in the usual way, there is no need to bring in homotopy classes at all.
Nov
27
comment Does the five lemma hold true for Lie algebras?
However, the category of Lie algebras is a semi-abelian category.
Nov
26
accepted Are cofibrant/fibrant replacements homotopically unique?
Nov
26
answered Are cofibrant/fibrant replacements homotopically unique?
Nov
26
comment Monoidal categories in which $\mathrm{Aut}(X \otimes Y) \cong \mathrm{Aut}(X) \sqcup \mathrm{Aut}(Y).$
Strictly speaking, this is the free strict monoidal category, of course. The free monoidal category has non-trivial unitors and associators.
Nov
25
revised Euler characteristic, genus and cohomology: a deep connection?
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Nov
25
revised Existence of projectives in the category of torsion abelian groups
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Nov
25
comment Are there some reference books or handbooks on homology and homotopy groups of every manifold which has been calculated?
Crossposted on MO.
Nov
25
comment tensor product and commutation, category theoretical argument
You could probably use the fact that filtered categories are sifted.