List questions from hom-functor | MathQA

How do you derive the adjoint's "naturality" condition as seen in MacLane & Moerdijk's book "Sheaves in Geometry and Logic"?

Published on 10 Jan 2022 - 17:52

$F$ left adjoint to $G \iff F,G$ define a functor from $\textbf{Arr}(\textbf{X}\times\textbf{A}) \to 2\times 1$ square CDs in $\textbf{Set}$?

Published on 12 Jan 2022 - 3:53

$(X^Y)^Z\cong X^{(Y+Z)}$ or $(X^Y)^Z\cong X^{(Y\times Z)}$?

Published on 12 Mar 2022 - 19:03

Weighted limits

Published on 23 Mar 2026 - 22:14

Characterizing Representable / Hom Functors via Universal Property

Published on 25 Jun 2022 - 11:33

Is the $Hom (-,k)$ functor exact?

Published on 20 Aug 2022 - 6:50

Finitely presentable objects in presheaves

Published on 26 Aug 2022 - 10:10

Bifunctoriality stronger than functoriality in each variable?

Published on 28 Aug 2022 - 21:41

the hom-functor is left exact: an equivalent condition

Published on 03 Oct 2022 - 16:40