Search Results

Increasingly harder question, but a reference for the first would be ok: Is the category of (symmetric?) monoidal categories closed for limits like products? Is it true that the underlying category …

Just for the sake of completeness, this can be done for infinity monoidal categories with the following trick. Infinity monoidal categories are precisely cocartesian fibrations over $N(Fin_*)$, which …

What about the classical theorem that the natural transformation $\eta$ witnessing the adjointess of two functions $F, G$: $$ \alpha_{X, Y} : Hom(FX, Y) \simeq Hom(X, GY) $$ is determined by the value …

$\DeclareMathOperator\cp{cp}$We will derive some additional necessary conditions from the following Observation: Let $\tau$ be a topology on $X$ and $\tau'$ a topology refining $\tau$. Suppose tha …

I recall that there was a theorem mimicking the change of variables' integral formula. Surprisingly, I can't find it on the Fosco Loregian book. The change of variables formula states that, if $f: E \ …

I stuck at a relatively simple thing of formalization in infinity setting. I use here the formalism of quasi categories, i.e. simplicial sets with inner horn fillings. Suppose $O^{\otimes}$ is an inf …

A recommendation: make drawings of cones! Note that by definition $$ (X_{/b})_n = Hom_b((\Delta^n)^{\triangleright},X)$$ Where $Hom_b$ means maps that sends the cone point to b. By Yoneda Lemma we c …

Let $M,N$ be a manifold and consider the presheaf of spaces $\textrm{Emb}(-, N)$ on the open sets of $M$. Classical embedding calculus produces a goodwillie tower $$ \ldots \rightarrow T_{k+1} \textrm …

In my limited perspective on the history of mathematics, I can name at least two big revolutions in Topology and Geometry (broadly construed): the introduction of Schemes in Algebraic Geometry, and th …