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 Sep13 comment Equalizers and Basic limit theorem in Category theory @KarlKronenfeld, that's precisely what I was missing, thanks. Care to write up an answer? Sep13 comment Equalizers and Basic limit theorem in Category theory But limits require that for any limit $X$ with arrow $f_i : X \rightarrow D_i$ in the limit and arrow $g : D_i \rightarrow D_j$ in the diagram, $f_j = g \circ f_i$. If we ignore extra $D_e : D_I \rightarrow D_J$ in the proof then it seems like there are arrows in the diagram (the ignored arrows) that could violate this equation. Sep13 asked Equalizers and Basic limit theorem in Category theory Aug4 revised Confusion about Homotopy Type Theory terminology added 17 characters in body Aug3 comment Confusion about Homotopy Type Theory terminology So the section immediately following dependent sums discusses coproduct types, which answers my first question. I'm still curious as to the nature of superexponential types. Are they inhabited by functions of multiple variables? Aug3 comment Confusion about Homotopy Type Theory terminology Neat. I suppose you could go a step further and say that there's a Successor type data Succ a = Zero | Succ a (known as Maybe to programmers), and then generalize sum types $A + B$ as dependent succession $Succ_{x:A} B$, and then generalize Succession as dependent unity and complete the pattern. Out of curiosity, what do you call independent types that generalize into dependent exponents (i.e. superexponential types), and what would they look like? Aug3 accepted Confusion about Homotopy Type Theory terminology Aug3 comment Confusion about Homotopy Type Theory terminology Oh. Neat. I feel silly now. Want to write that up as an answer? Aug3 asked Confusion about Homotopy Type Theory terminology Jun17 comment How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? My confusion was rooted in the fact that the function is not continuously differentiable. Now I feel silly. Jun17 accepted How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Jun17 answered How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Jun12 revised How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Typo fix: the lt/ge signs were swapped. Jun12 suggested approved edit on How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Jun12 comment How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Sure -- but is their a unified equation for the function? It feels like there should be. Jun12 asked How do you combine the bipartite function $y=2^{x-1}$ for $x\lt0$ & $y=1-2^{-x-1}$ for $x\ge0$? Jun10 awarded Yearling Jun10 comment Why do we write second derivatives like $\frac{d^2x}{dt^2}$ This makes very little sense to me. How come we can separate the $d$ from $x$ in $dx$, but we can't separate the $d$ from $t$ in $dt$? What are these $d$ things anyway, and why do we treat the one attached to $x$ differently from the one attached to $t$? Jun10 asked Why do we write second derivatives like $\frac{d^2x}{dt^2}$ May23 awarded Popular Question