We first take a whimsical look at a couple of questions relating to categories as generalized posets. Then we study the question of functorial choice of pullbacks. Finally, we consider a simple question in basic category theory, with an elementary solution which is surprisingly difficult to generalize to 2-categories.
Keywords: Adjoint functor, preorder, functorial pullbacks, 2-category
2020 MSC: 18A40, 18B35, 18A30, 18N10, 18D30
Theory and Applications of Categories, Vol. 36, 2021, No. 6, pp 171-200.