# Difference between revisions of "Summer stacks"

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=== Introduction === | === Introduction === | ||

Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle | Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle | ||

+ | |||

+ | A: I figured it out myself :) The fiber product is along s and t, which I assume means that the elements of the fiber product are pairs (f,g) such that t(f)=s(g). Thus it's okay for m to only be multiplied on those elements because that's all there is. | ||

=== Chapter 1 === | === Chapter 1 === |

## Revision as of 13:57, 25 May 2012

This is the page for the 2012 Summer stacks reading group.

## Resources

The book in progress of Behrend, Fulton, Kresch and other people is available here: [1]

Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.

The Stacks Project: [2]

## Milestones

6/1 Finish Chapter 1

6/14 Finish Chapter 2

6/29 Finish Chapter 3

7/14 Finish Chapter 4

7/28 Finish Chapter 5

## Comments, Questions and (hopefully) Answers

### Introduction

Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle

A: I figured it out myself :) The fiber product is along s and t, which I assume means that the elements of the fiber product are pairs (f,g) such that t(f)=s(g). Thus it's okay for m to only be multiplied on those elements because that's all there is.

### Chapter 1

Q:

A:

### Chapter 2

### Chapter 3

### Chapter 4

### Chapter 5

## Summer plans

If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:

Ed: Leaving June 2, back around August 1.

Jeff: Leaving June 17, back July 8.

Evan: Leaving May 22, back June 20.

Christelle: Leaving June 24, back July 20, leaving August 4.

David: Leaving June 17, back July 8. Leaving July 31, back August 14th.