preserved colimit

1. Definition

Let 20231014-preserved_colimit_2d5d1c2bfbb1a2fca757f722875cd0787290c048.svg be categories, 20231014-preserved_colimit_68c2e4f467e25e7fe0a812a64e0b6a3501aa2e53.svg a diagram and 20231014-preserved_colimit_570624dc5b21d1f0a192cc0f7dad2a4f870badf0.svg a functor. Suppose 20231014-preserved_colimit_bf132eeee4342dcb0a23710e6d8bafe1b0466532.svg together with morphisms 20231014-preserved_colimit_85deed5f910d5e8e6e90e4cf080ecc4bc7c42c48.svg is a colimit, then 20231014-preserved_colimit_c766db72f74b8081e5c597a048bac99bb6222c6c.svg is preserved under the functor, if the induced morphism between colimits and functor is an isomorphism

20231014-preserved_colimit_d3cd5eb071a0500e621e81a2f6a1654ea70d08ef.svg

Note that 20231014-preserved_colimit_5aa45365123ab142cc7f9e5384ce7eafbdaa9be3.svg with 20231014-preserved_colimit_d3d64e21d8118b588a5cbc4f0d0e0feb0db37084.svg is a limit.

see preserved limit

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 18:36