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Nov
26
revised Deeper studies in Category Theory: suggestions and references.
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Nov
26
revised Deeper studies in Category Theory: suggestions and references.
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Nov
26
comment Deeper studies in Category Theory: suggestions and references.
The arXiv version is out-of-date. The latest version can be found on Lurie's website.
Nov
25
revised On the definition of the direct sum in vector spaces
added 59 characters in body; edited tags
Nov
25
comment Existence of inaccessible cardinals implies the consistency of ZFC
Equivalently, you can verify that $V_\kappa$ is a model of ZFC, where $\kappa$ is an inaccessible cardinal.
Nov
25
comment How strong is the analogy between spectra and abelian groups?
If you could expand on that with references, that would be much appreciated!
Nov
25
comment Could the concept of “finite free groups” be possible?
The only free group that is finite is the trivial group. What on earth could a "finite free group" be?
Nov
25
comment colimit on presheafs
Or otherwise restrict to finite connected diagrams. Then it is true: the colimit of a finite connected diagram can indeed be constructed by iterated pushouts. The proof is ugly, however.
Nov
25
comment colimit on presheafs
What you claim cannot possibly be true: how do you use just pushouts to construct the colimit of a diagram with more than one connected component?
Nov
25
comment Definition of a one-connected manifold?
I have seen "1-connected" as an abbreviation for "simply connected".
Nov
25
comment Examples of canonical projections that are not epimorphisms and canonical injections that are not
Your claim is incorrect: the projection $X \times \emptyset \to X$ is surjective if and only if $X = \emptyset$.
Nov
24
comment What is homotopy in $(\infty,1)$-categories (as weak Kan complexes)
You basically choose two faces of the $(n + 1)$-simplex to be the source and target and require the remainder to be degenerate in the appropriate sense. The case $n = 1$ is discussed in any introduction to quasicategories.
Nov
24
comment What is homotopy in $(\infty,1)$-categories (as weak Kan complexes)
A homotopy between $n$-cells in a quasicategory is a special kind of $(n + 1)$-cell.
Nov
24
awarded  Nice Answer
Nov
24
answered What are presentable categories?
Nov
23
comment Are these categories toposes?
None of the above: all of these categories are not even cartesian closed.
Nov
22
comment Exact sequence of sheaves with non exact sequence of global sections
What's wrong with the exponential sequence as an example?
Nov
22
comment Is every complex (smooth) manifold a scheme?
Yes: schemes are by definition algebraic.
Nov
22
comment Is every complex (smooth) manifold a scheme?
The unit disc in $\mathbb{C}$ is surely a Riemann surface but not a complex variety. (Note, it is not isomorphic to $\mathbb{C}$ as a Riemann surface!)
Nov
22
comment Why are there no naturality condition in definition of exponential in a category?
Awodey's formulation includes the $\epsilon$, which implies naturality.