cokernel (category theory)

1. Definition

A cokernel is a kernel in the opposite category

2. Explicite

Let 20230827-cokernel_category_theory_760824120891fc757bc0445145b027d09b237baa.svg be a category with a zero object 20230827-cokernel_category_theory_0f18e978368c4f73a67ad13f1c1c733366f7cfee.svg. Then the 20230827-cokernel_category_theory_1ed2c8795b12dbf5ab2be99d3f288390cd33a29e.svg for a morphism 20230827-cokernel_category_theory_2f45efa620434a1c03713e6c4cc5527b5f5312bb.svg - if it exists - is defined as pushout

20230827-cokernel_category_theory_956d3fe68467b3deede58c1ffcded146653f6d77.svg

resp. a coequalizer

20230827-cokernel_category_theory_c0816b2d47834c620ce0ed5133ea511f74a8d474.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 15:59