# Elementary quotient completion

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3898-1980.

dept.math [at] unitn.it

**Luogo: **Seminar Room (ground floor) – Department of Physics

**Ore**: 10.00

### Relatore:

**Davide Trotta**(PhD student University of Trento Dept. of Mathematics)

### Abstract:

In the first part of the seminar we introduce the notion of primary and elementary doctrine and we explain how it is related to logic.

In the second one we show how any elementary doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients.

We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, the other forces extensionality of morphisms.

We also explain how each construction preserves comprehension.

**Contact person: **Roberto Zunino