The formal dual to the pushout product (frequently considered in the context of enriched model category theory) does not have a widely established name, but plausibly deserves to be called the pullback powering operation. Note that it sometimes called pullback hom.
More precisely, a pushout product is defined with respect to a functor of the form , while a pullback power is defined with respect to a functor of the form or , of the sort that would be the right adjoints in a two-variable adjunction.
Pullback powers and pushout products are related to factorization systems by the Joyal-Tierney calculus.
Let be category with finite limits and let
a functor (out of the product category of the opposite category of with itself). Then for
and
two morphisms in , their pullback powering is the morphism
into the evident fiber product on the right.
Last revised on December 18, 2022 at 17:19:10. See the history of this page for a list of all contributions to it.