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answered  Which graphs embedded in surfaces have symmetries acting transitively on vertexedge flags? 
Feb
25 
awarded  Popular Question 
Feb
16 
comment 
A morphismrevealing category?
I'm not quite sure what you mean by "revealed morphism", but I think the idea you are getting at is that many concrete categories can be embedded into the subset bifibration in a functorial way. I added a bit more clarification to the answer. 
Feb
16 
revised 
A morphismrevealing category?
suggest the general setup for concrete categories 
Feb
16 
revised 
A morphismrevealing category?
fixed variance 
Feb
16 
answered  A morphismrevealing category? 
Feb
3 
answered  The sourcesideopposite of the arrow category 
Jan
27 
comment 
NonCartesian Monoidal Model Structure on a Slice Category
I'm also very interested in the history of this construction. Let me mention that (1) and (2) can also be formulated as follows: for any monoidal closed functor $p : \mathcal{E} \to \mathcal{B}$ which is also a Grothendieck bifibration, if $(M,\otimes,1) \in \mathcal{B}$ is a monoid in the basis, then its fiber $\mathcal{E}_M$ is monoidal closed. This approach is something PaulAndré Melliès and I have looked at in recent years. One advantage of this formulation is that it also covers the Day construction of a monoidal closed structure on the presheaf category over a (pro)monoidal category. 
Oct
23 
awarded  Yearling 
Sep
22 
answered  Classification of tangles? 
May
29 
comment 
How true are theorems proved by Coq?
@DavidRoberts: I am not sure the precise reference, but I know this is something that Peter Hancock and Anton Setzer have studied deeply. Here are some slides by Peter Hancock, which end with the claim in question: cs.swan.ac.uk/~csetzer/russell08/slides/hancock.pdf 
May
9 
comment 
Table of planar connected graphs
@this_is_an_apple such illustrated tables are included in the atlas by Jackson and Visentin I referenced above. Since you are considering planar graphs with multiple edges up to embeddingpreserving isomorphism, it sounds like the objects you are interested in are precisely what are known as "planar maps". 
May
9 
answered  Table of planar connected graphs 
Apr
1 
answered  Embedding of classical into intuitionistic linear logic 
Apr
1 
comment 
Conservativity of multiplicative linear logic over intuitionistic multiplicative linear logic
there are a few references I might suggest, depending on what exactly you have in mind. But since that is a different question, I think the modus operandi for this site would be to accept my answer to your first question (if you think it is resolved), then post your second question separately, with a new title. That way it might also get noticed by people who didn't happen to click on the first question. 
Mar
31 
answered  Conservativity of multiplicative linear logic over intuitionistic multiplicative linear logic 
Nov
22 
awarded  Civic Duty 
Oct
23 
awarded  Yearling 
Oct
5 
answered  Has philosophy ever clarified mathematics? 
Oct
4 
accepted  How to understand a rooting of a dessin d'enfant? 