@DylanWilson Thanks! I guess I want to compute Tor in the category of C-modules. I guess I can use a similar argument with the right adjoint f^*, which is monoidal in my situation I believe.

I guess the users of this room might be able to help with this, so I'll ask here.

Is the tag algebraic-cobordism useful? I am asking because it is currently used on a single question. Tags which have only a single occurrence and empty tag-wiki are removed by an automated process after 6 months.

@MartinSleziak Dunno if it is an appropriate tag, but it is certainly a legitimate math topic, and there are other questions that could be tagged with it (for example mathoverflow.net/questions/235033/is-mgl-an-h-mathbbz-algebra , mathoverflow.net/questions/283311/… and mathoverflow.net/questions/111849/…), although they tend to have already enough tags

Thanks for the response. In two of the linked questions, the five slots for tags are already taken.

We'll see what the others think about this tag. If the tag is worth keeping, maybe somebody will create the tag-wiki.

(Hopefully it's not off topic) Can someone explain to me (in geometrical terms) what's the difference between the virtual dimension and the dimension of a moduli space of, say J-hol curves into a symplectic manifold M?

I keep on reading that the virtual one is the expected one, somehow the correct one. Problem is I'm not aware of why should I expect a dimension of my object different that the one given to me by say the Riemann-Roch/AS-Index theorem. I must be missing something then

@Riccardo I'm not familiar with J-hol curves that much although from what I understand "expected dimension" in this context means that the moduli space can be expressed as some sort of intersection of other (maybe infinite dimensional) manifolds (e.g. the zero section of a non-linear differential operator) and then the "expected dimension" is the number you get calculating the dimension of the intersection as though the intersection was transverse)

While the actual dimension may be different due to the intersection not being transverse.

For example if we intersect a line and a hyperplane in $\mathbb{R}^3$ s.t. the line lies inside the plane we get the line back again which is 1 diensional. The "expected dimension" however is $dim(\mathbb{R}^3) - codim(line) - codim(plane) = 3 - 2 - 1 = 0$. If the line would be transverse to the plane we would get just a point which is 0 dimensional so in this case the numbers match.

the "zero set"" not "zero section up there in the second row

Anyone know if there is a classification of categories V for which V-Cat is V-enriched (under the usual assumptions on V itself)?