A finite product is a product (Cartesian product) of a finite number of factors.
Finite products are generated from the empty product (the terminal object) and binary products (those with two factors, often – but not always – understood by default under “product”.)
Similarly a finite coproduct is a coproduct of a finite number of summands. This is generated from the empty coproduct (the initial object) and binary coproducts.
(categories with finite products are cosifted)
Let be a small category which has finite products. Then is a cosifted category, equivalently its opposite category is a sifted category, equivalently colimits over with values in Set are sifted colimits, equivalently colimits over with values in Set commute with finite products, as follows:
For to functors on the opposite category of (hence two presheaves on ) we have a natural isomorphism
Last revised on May 20, 2023 at 08:40:46. See the history of this page for a list of all contributions to it.