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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
New page displayed category.
I created article cotopology including a redirect from cocompact space.
I separated p-derivation from Fermat quotient.
I’ve just edited topological concrete category to correct the claim that topological functors create limits, which is not quite true: for instance, the forgetful fails to reflect limits because choosing a finer topology on the limit vertex yields a non-limiting cone with the same image in . This is correctly reported on wikipedia and in Joy of Cats, p. 227.
It is true that topological functors allow you to calculate limits using the image of the diagram under the functor, which is quite powerful. In Joy of Cats, a topological functor is said to “uniquely lift limits” (definition p. 227, proven p. 363). There doesn’t seem to be an nlab page for this property – I suppose it’s not much used by most category theorists.
created over-topos
I have tried to brush-up Kleisli category; also made Kleisli composition redirect to it and cross-linked with monad (in computer science)
at monoidal adjunction the second item says
while the left adjoint is necessarily strong
but should it not say
while the left adjoint is necessarily oplax
?
I added the definition of uniform space in terms of covering families. But I don’t know the covering version of the constructive “axiom (0)”.
created arithmetic jet space, so far only highlighting the statement that at prime these are (regarded so in Borger’s absolute geometry by applying the Witt ring construction to it).
This is what I had hoped that the definition/characterization would be, so I am relieved. Because this is of course just the definition of synthetic differential geometry with regarded as the th abstract formal disk.
Well, or at least this is what Buium defines. Borger instead calls itself already the arithmetic jet space functor. I am not sure yet if I follow that.
I am hoping to realize the following: in ordinary differential geometry then synthetic differential infinity-groupoids is cohesive over “formal moduli problems” and here the flat modality is exactly the analog of the above “jet space” construction, in that it evaluates everything on formal disks. Moreover, canonically sits in a fracture suare together with the “cohesive rationalization” operation and hence plays exactly the role of the arithmetic fracture square, but in smooth geometry. I am hoping that Borger’s absolute geometry may be massaged into a cohesive structure over the base that makes the cohesive fracture square reproduce the arithmetic one.
If Borger’s absolute direct image were base change to followed by the Witt vector construction, then this would come really close to being true. Not sure what to make of it being just that Witt vector construction. Presently I have no real idea of what good that actually is (apart from giving any base topos for , fine, but why this one? Need to further think about it.)
while writing out the proof of the fundamental product theorem in K-theory I had occasion to record that
Created doctrinal adjunction. The page could probably use some examples and/or fleshing out.
I put a disambiguation block at the top of inverse image to point to preimage.
created induced metric, just for completeness
Created parametric right adjoint.
created diagram chasing lemmas - contents (with some information on what implies what) and included it as a floating TOC into the relevant entries.
I had started an entry “exponentiation” but then thought better of it and instead expanded the existing exponential object: added an examples-section specifically for and made some remarks on exponentiation of numbers.
Added Eric’s illustrations to the Idea-section at Yoneda embedding.
Although referred to in a couple of place, it seems we had no entry for spatial topos, so I’ve made a start.
A long time ago we had a discussion at graph about notions of morphism. I have written an article category of simple graphs which collects some properties of the category under one of those definitions (corresponding better, I think, to graph-theoretic practice).
Created twosets20170617. Contains an svg illustration of a full subcategory of consisting of a terminal object and a two-element set. Uses the convention that an identity arrow is labelled by its object. Intended for use in some graph-theoretical considerations from an nPOV. Sufficiently general to be possibly of use in some other nLab articles too.
Created a stub for internal type theory to collect some references. At some point we could move more from Mike’s blog post.
created amazing right adjoint
I wrote down some standard facts about nonstandard models of Peano arithmetic at nonstandard model of arithmetic, and spelled out two proofs (really the same proof) that the ordering on the nonstandard part is always dense.
I changed “irreflexive graph” to “directed graph” (aka quiver), as such a presheaf is more commonly known. (Irreflexive to my mind means loops at a vertex are forbidden.)
Somehow we didn’t yet have a page about pseudo-distributive laws, so I made a stubby one with a few examples and references.
Comment/question on terminology in the (?,1)-case at regular epimorphism