categorical product

1. Definition

Let 20230404141718-categorical_product_760824120891fc757bc0445145b027d09b237baa.svg be a category and 20230404141718-categorical_product_af773f204019917a22fb1e343acbd7b20d384f5a.svg a set of objects, then the categorical product is - if it exists - an object

20230404141718-categorical_product_d18d7b8570935ae2dd56a0bc5922c0ad0b732f67.svg

with morphisms

20230404141718-categorical_product_b1c042de271324f3130cf78f689200fa58e080ee.svg

such that for every diagram

20230404141718-categorical_product_37d63aa593bca61c06a07ea1a347988bc53c24cb.svg

there exists a unique morphism 20230404141718-categorical_product_eab647e5edee3de9c5f2693d3ab281e8261cd2b9.svg, making the diagram commute

20230404141718-categorical_product_91ff12697e3a1bd5e6a28a94458416e3ea87be02.svg

Note, that most of the time, a small product is meant see also:

Date: nil

Author: Anton Zakrewski

Created: 2024-10-12 Sa 23:12