injective object

1. Definition

A injective object is a projective object in the opposite category

2. Explicite

Let 20230903-injective_object_760824120891fc757bc0445145b027d09b237baa.svg be a category and 20230903-injective_object_925e403e9996479c296d38d7b008fe7338518037.svg Then 20230903-injective_object_9c8bdb9f6ad11c13881249483fa93b024273b477.svg is said to be injective, if for every object 20230903-injective_object_3f0d1a599184c702673acd54eb025009a6fee805.svg and monomorphism 20230903-injective_object_3372f1fd63612d438da7a319db8f10495c88a2dd.svg each morphism 20230903-injective_object_dae4bfc49ff51a21300a7d6481a369f8bae10b0b.svg factors through 20230903-injective_object_9485e48332c47acf9b1f77913ef6fd31df3dc164.svg, i.e.

20230903-injective_object_c511fc0c3607e8f34970ab0c843ab2ff0f2cdedc.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 18:09