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Sep
26
comment Does Localization Commute with Direct/Inverse Limits
It's actually true for all colimits, because localisation is a left adjoint.
Sep
25
comment When is $\infty$ a critical point of a rational function on the sphere?
You can use either function if $f(\infty) \notin \{ 0, \infty \}$.
Sep
25
comment On Lemma 4.1 of Hartshorne's algebraic geometry text
It's worth remarking that the diagonal is closed even though $Y$ isn't Hausdorff!
Sep
25
answered When is $\infty$ a critical point of a rational function on the sphere?
Sep
24
answered Isomorphisms in the localization of a category
Sep
24
revised Invertible sheaves and invertible classes in the Picard group
deleted 12 characters in body
Sep
24
comment what is this categorical construction?
Well, if you don't demand that the morphism making the diagrams commute be unique then it isn't necessarily a product. You could call it a "weak" product.
Sep
24
answered what is this categorical construction?
Sep
24
comment Equiv. of Cats. Preserves Product
(4) requires care: one must avoid talking about equalities of objects for that to be true.
Sep
23
comment Does $\mathsf{Man}$ possess countable products?
@MartinBrandenburg I suspect the OP is asking about possibly-infinite-dimensional manifolds, given the mention of "locally convex spaces".
Sep
23
revised Symmetric monoidal products that preserve limits and colimits
edited body
Sep
23
revised Why are simplicial categories useful?
added 1 characters in body
Sep
23
comment Why are simplicial categories useful?
My notes are still being updated. The project page is here.
Sep
23
comment Symmetric monoidal products that preserve limits and colimits
The cartesian product in a cartesian closed category preserves colimits in each variable separately, but it doesn't preserve products!
Sep
23
comment Left Inclusion is Not Equal to Right Inclusion
The only dependent function here is defined by induction on equality, not induction on coproducts.
Sep
23
answered Why are simplicial categories useful?
Sep
23
comment characterization of projective/injective/flat modules via $\operatorname{Hom}$ and $\otimes$
No, you misunderstand. ${-} \otimes M$ being right exact means that it sends a short exact sequence $0 \to A \to B \to C \to 0$ to a right exact sequence $A \otimes M \to B \otimes M \to C \otimes M \to 0$, which is much stronger than merely preserving epimorphisms.
Sep
23
answered topologically equivalent spaces
Sep
22
answered Left Inclusion is Not Equal to Right Inclusion
Sep
22
answered What does it mean to have exact derived functors?