## Bulletin of the Belgian Mathematical Society - Simon Stevin

### When does secat equal relcat ?

#### Abstract

In [3] the authors introduced a {\em relative category} for a map that differ from the {\em sectional category} by just one. The relative category has specific properties (for instance a homotopy pushout does not increase it) which make it a convenient tool to study the sectional category. The question to know when secat equals relcat arises. We give here some sufficient conditions. Applications are given to the {\em topological complexity}, which is nothing but the sectional category of the diagonal.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 5 (2013), 769-776.

Dates
First available in Project Euclid: 25 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1385390762

Digital Object Identifier
doi:10.36045/bbms/1385390762

Mathematical Reviews number (MathSciNet)
MR3160587

Zentralblatt MATH identifier
1288.55001

#### Citation

Doeraene, Jean-Paul; El Haouari, Mohammed. When does secat equal relcat ?. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 769--776. doi:10.36045/bbms/1385390762. https://projecteuclid.org/euclid.bbms/1385390762