glueing lemma for pullbacks

1. Proposition

Let 20231102-glueing_lemma_for_pullbacks_760824120891fc757bc0445145b027d09b237baa.svg be a category, and

20231102-glueing_lemma_for_pullbacks_d6538340ea90dfc1e6f24eebeec3ea995055dc22.svg

be a commutative diagram, such that

20231102-glueing_lemma_for_pullbacks_162979d279091a7ea3b4c5c55c952b58e6ed73cb.svg

and

20231102-glueing_lemma_for_pullbacks_19cc50bcfa2d8b6c35a61f36691ab9bb0e6ea1ca.svg

are pullbacks Then

20231102-glueing_lemma_for_pullbacks_784b41fa7fe7801c42234e9765bb98366ba14888.svg

is also a pushout

2. Proof

dually to glueing lemma for pushouts.

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 18:58