Jonathan Chiche

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Name	Jonathan Chiche
Member for	3 years
Seen	1 hour ago
Website	math.jussieu.fr/~chiche
Location	Paris
Age	27

PhD student (since September 2010) under the supervision of Georges Maltsiniotis in Paris. My research subject is the homotopy theory of 2-categories.

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Has the mathematical content of Grothendieck’s “Récoltes et Semailles” been used?

dec 14 10 at 8:51 Minhyong Kim 7,179●5●30●52

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In which situations can one see that topological spaces are ill-behaved from the homotopical viewpoint?

big-list homotopy-theory at.algebraic-topology gt.geometric-topology ct.category-theory

feb 7 12 at 10:30 Ronnie Brown 5,217●17●20

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710

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What has happened to Lang’s Files and other political texts?

reference-request pedagogy politics soft-question

nov 27 at 14:00 Jonathan Chiche 1,411●1●7●16

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315

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Is there any elementary text unravelling the definitions of 2-category, lax functor and lax transformation, allowing people who do not know in the first place what these things are to really understand the definitions?

reference-request higher-category-theory pedagogy

jan 9 12 at 9:01 Jonathan Chiche 1,411●1●7●16

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223

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What is the history of the notion of subdivision of categories?

ho.history-overview at.algebraic-topology ct.category-theory simplicial-stuff higher-category-theory

jul 31 at 8:43 Jonathan Chiche 1,411●1●7●16

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333

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How do various notions of natural transformation relate to various notions of homotopy in $2Cat$?

homotopy-theory ct.category-theory higher-category-theory

jan 3 12 at 9:01 Jonathan Chiche 1,411●1●7●16

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309

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Does the category of strict $2$-categories together with Dwyer-Kan equivalences provide a model for $(\infty,1)$-categories?

homotopy-theory higher-category-theory ct.category-theory simplicial-stuff

dec 25 11 at 12:13 Chris Schommer-Pries 10.2k●1●17●57

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234

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Where is it rigorously stated and proved that the definition of lax functor implies that the generalized cocycle condition holds for an arbitrary number of composable $1$-cells?

ct.category-theory reference-request

nov 2 at 21:02 Buschi Sergio 1,799●1●3●8

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382

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Is there a standard name for a 2-category which has an object z such that, for every object x, the category Hom(x,z) has a terminal object?

terminology ct.category-theory homotopy-theory

oct 22 at 7:45 Jonathan Chiche 1,411●1●7●16

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What should be the terminology regarding symmetries in 2-Cat?

terminology ct.category-theory

nov 10 at 19:53 Jonathan Chiche 1,411●1●7●16

Answers

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The half-life of a theorem, or Arnold’s principle at work

Is there a high-concept explanation for why “simplicial” leads to “homotopy-theoretic”?

What is the homotopy theory of categories?

Conjectures in Grothendieck’s “Pursuing stacks”

Find weak equivalences from fibrations and cofibrations

Is there a topos theoretic interpretation/proof of Quillen’s Theorem A?

A (too easy) normalization of a lax-funtor between 2-categories ?

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Jonathan Chiche

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Questions

Has the mathematical content of Grothendieck’s “Récoltes et Semailles” been used?

In which situations can one see that topological spaces are ill-behaved from the homotopical viewpoint?

What has happened to Lang’s Files and other political texts?

Is there any elementary text unravelling the definitions of 2-category, lax functor and lax transformation, allowing people who do not know in the first place what these things are to really understand the definitions?

What is the history of the notion of subdivision of categories?

How do various notions of natural transformation relate to various notions of homotopy in $2Cat$?

Does the category of strict $2$-categories together with Dwyer-Kan equivalences provide a model for $(\infty,1)$-categories?

Where is it rigorously stated and proved that the definition of lax functor implies that the generalized cocycle condition holds for an arbitrary number of composable $1$-cells?

Is there a standard name for a 2-category which has an object z such that, for every object x, the category Hom(x,z) has a terminal object?

What should be the terminology regarding symmetries in 2-Cat?

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