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Jardine's article Simplicial objects in a Grothendieck topos

Example of a small toposOriginal article on the Grothendieck groupTwo questions about monomorphisms and pullbacks in a Grothendieck toposProjective Objects in a ToposIs the cartesian product of objects in an elementary topos cancellative?About certain regular epimorphisms in a Grothendieck ToposWhere to learn about model categories?Is every topos equivalent to a full subtopos of U-small objects in another topos?Homotopy classes of maps inside a Grothendieck toposForcing in sheaf models of set theory - where do the “generics” disappear to?

2

$begingroup$

In the epilogue of Maclane and Moerdijk's Sheaves and Logic, it gives some overview of the connection of topoi and algebraic topology to simplicial method.

One reason that
simplicial techniques apply well to topoi is that the simplicial objects in
a Grothendieck topos have such a closed model structure, as shown by
A. Joyal in an elegant, as yet unpublished, letter (1984) to Grothendieck.
A related older paper is Brown (1973), which gives for simplicial objects
in a sheaf topos a weaker "local" version of a Quillen model structure.
...

Jardine's (1986) paper
describes in more detail the methods from the letter by Joyal mentioned
above, and applies these in the context of Suslin's computations for
the K-groups of an algebraically closed field. Thomason (1985) uses
simplicial techniques for topoi to compare algebraic and topological K-
theory.

I'm trying to look at the article Jardine (1986) Simplicial objects in a Grothendieck topos but found that I have no access to it even though I'm in a university institute. But I also have another article by Jardine Generalised sheaf cohomology theories which is more latest and it quotes Jardine (1986). Does this article cover the main idea in Jardine (1986)? Or can anyone provide some latest references in this area: topos theory and algebraic topology?

reference-request algebraic-topology sheaf-cohomology topos-theory

share|cite|improve this question

asked Mar 11 at 19:19

NickyNicky

1037

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Jardine published a book in 2015 (Local Homotopy Theory) that describes all of this in much greater detail.
  $endgroup$
  – Dmitri Pavlov
  Mar 12 at 1:07
  
  

  
  
  
  

add a comment | 

2

$begingroup$

In the epilogue of Maclane and Moerdijk's Sheaves and Logic, it gives some overview of the connection of topoi and algebraic topology to simplicial method.

One reason that
simplicial techniques apply well to topoi is that the simplicial objects in
a Grothendieck topos have such a closed model structure, as shown by
A. Joyal in an elegant, as yet unpublished, letter (1984) to Grothendieck.
A related older paper is Brown (1973), which gives for simplicial objects
in a sheaf topos a weaker "local" version of a Quillen model structure.
...

Jardine's (1986) paper
describes in more detail the methods from the letter by Joyal mentioned
above, and applies these in the context of Suslin's computations for
the K-groups of an algebraically closed field. Thomason (1985) uses
simplicial techniques for topoi to compare algebraic and topological K-
theory.

I'm trying to look at the article Jardine (1986) Simplicial objects in a Grothendieck topos but found that I have no access to it even though I'm in a university institute. But I also have another article by Jardine Generalised sheaf cohomology theories which is more latest and it quotes Jardine (1986). Does this article cover the main idea in Jardine (1986)? Or can anyone provide some latest references in this area: topos theory and algebraic topology?

reference-request algebraic-topology sheaf-cohomology topos-theory

share|cite|improve this question

asked Mar 11 at 19:19

NickyNicky

1037

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Jardine published a book in 2015 (Local Homotopy Theory) that describes all of this in much greater detail.
  $endgroup$
  – Dmitri Pavlov
  Mar 12 at 1:07
  
  

  
  
  
  

add a comment | 

$begingroup$

In the epilogue of Maclane and Moerdijk's Sheaves and Logic, it gives some overview of the connection of topoi and algebraic topology to simplicial method.

One reason that
simplicial techniques apply well to topoi is that the simplicial objects in
a Grothendieck topos have such a closed model structure, as shown by
A. Joyal in an elegant, as yet unpublished, letter (1984) to Grothendieck.
A related older paper is Brown (1973), which gives for simplicial objects
in a sheaf topos a weaker "local" version of a Quillen model structure.
...

Jardine's (1986) paper
describes in more detail the methods from the letter by Joyal mentioned
above, and applies these in the context of Suslin's computations for
the K-groups of an algebraically closed field. Thomason (1985) uses
simplicial techniques for topoi to compare algebraic and topological K-
theory.

I'm trying to look at the article Jardine (1986) Simplicial objects in a Grothendieck topos but found that I have no access to it even though I'm in a university institute. But I also have another article by Jardine Generalised sheaf cohomology theories which is more latest and it quotes Jardine (1986). Does this article cover the main idea in Jardine (1986)? Or can anyone provide some latest references in this area: topos theory and algebraic topology?

reference-request algebraic-topology sheaf-cohomology topos-theory

share|cite|improve this question

asked Mar 11 at 19:19

NickyNicky

1037

$endgroup$

share|cite|improve this question

asked Mar 11 at 19:19

NickyNicky

1037

share|cite|improve this question

asked Mar 11 at 19:19

NickyNicky

1037

asked Mar 11 at 19:19

NickyNicky

1037

asked Mar 11 at 19:19

NickyNicky

1037