stability under pullbacks

1. Definition

Let 20231215-stability_under_pullbacks_760824120891fc757bc0445145b027d09b237baa.svg be a category. Some type of morphisms is said to be stable under pullbacks, if for 1 objects 20231215-stability_under_pullbacks_241be2f7b2e1ed205951d9f74bb29dd69f4888cd.svg

  1. a morphism 20231215-stability_under_pullbacks_dae4bfc49ff51a21300a7d6481a369f8bae10b0b.svg of the certain type
  2. any morphism 20231215-stability_under_pullbacks_d073c75658633ced9b9059022a1a00d381ba55fd.svg

it holds for the pullback, if it exists,

20231215-stability_under_pullbacks_2f940b4ac6ae6b2496843caaa14f596de34dc133.svg

that 20231215-stability_under_pullbacks_40eb88aa42cf30aa245260053e0779957d3a458c.svg satisfies the type

20231215-stability_under_pullbacks_a9a7b86aae571df4a2d7cc66cf7a4b5cbbd02ebf.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 23:51