Pushout example sentences

"Pushout" Example Sentences

1. The pushout of the functor from sets to groups is the category of abelian groups.
2. In category theory, the pushout is a binary operation on morphisms.
3. A pushout can be thought of as gluing two objects together along a common subobject.
4. The pushout of two maps f and g is the colimit of a certain diagram.
5. The pushout of a diagram D is characterized by a universal property.
6. To compute a pushout, one needs to find a suitable coequalizer.
7. A diagram has a pushout if and only if it is a coequalizer.
8. The pushout of two parallel maps f and g is denoted by f ∐ g.
9. The pushout of two maps f and g is the coproduct of two objects.
10. The pushout of two maps is also known as the pushout product.
11. The pushout of a morphism f along a monomorphism m is unique up to isomorphism.
12. In topology, the pushout of two maps is often used to construct new spaces.
13. The pushout of a morphism f along a zero morphism is just f itself.
14. The pushout of a pullback square is a commutative square.
15. The pushout of a diagram is sometimes called a cocone.
16. The pushout of a diagram can be computed using the coend formula.
17. The pushout of an idempotent morphism is just the morphism itself.
18. A pushout square is a square that can be completed to a commutative diagram.
19. The pushout of a diagram D is denoted by D ∨.
20. The pushout of a diagram is said to be functorial if it commutes with all colimits.
21. The pushout of a diagram is a non-commutative operation in general.
22. The pushout of a diagram is said to be stable under pullbacks if it commutes with them.
23. The pushout of a diagram is said to be stable under monomorphisms if it commutes with them.
24. The pushout of a diagram is said to be functorially cofibrant if it commutes with pushouts along cofibrations.
25. The pushout of a diagram is said to be functorially fibrant if it commutes with pullbacks along fibrations.
26. A pushout can be constructed using a colimit of a certain zigzag.
27. The pushout of a diagram can be computed using a limit of coequalizers.
28. The pushout of a diagram is often denoted by a symbol like ∐ or ⊔.
29. The pushout of a diagram can be defined as the coequalizer of two maps.
30. The pushout of a diagram can be characterized by a universal property as the colimit of a certain diagram.

Common Phrases

1. The pushout of two sets;
2. Pushout diagrams in category theory;
3. Applying the pushout functor;
4. The existence of pushouts;
5. Identifying pushout objects;
6. Pushing out morphisms in algebraic geometry;
7. Constructing a pushout square;
8. Pushout properties and examples.