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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 27th 2013
   • (edited Jun 27th 2013)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexFor some reason (related to idle wondering about a tangent category to a tangent category), I looked at [Romie Banerjee's](http://ncatlab.org/nlab/show/Romie+Banerjee) 'Categories of modules and their deformations' ([arxiv](http://arxiv.org/abs/1212.2083)). It has >Definition 4.1. ([6]) An ∞-prestack F has an obstruction theory if >(i) F is infinitesimally cohesive >(ii) F has a cotangent complex So I was interested to see the uptake of Urs' 'infinitesimal cohesion', but [6] points to Toen and Vezzosi's Homotopical Algebraic Geometry II ([arxiv](http://arxiv.org/abs/math/0404373)). I guess the reference is to their definition 1.4.2.1 >(2) A stack F has an obstruction theory (relative to (C, C0,A)) if it has a (global) cotangent complex and if it is infinitesimally cartesian (relative to (C, C0,A)). Is Banerjee suggesting then that infinitesimally cartesian and infinitesimally cohesive are the same? But the latter applies to $\infty$-toposes not stacks. Strange, n'est-ce pas? (EDIT: Oh, I see other people are using it differently, e.g., Lurie in DAG-XIV, Definition 2.1.9. Disambiguation needed?)

   For some reason (related to idle wondering about a tangent category to a tangent category), I looked at Romie Banerjee’s ’Categories of modules and their deformations’ (arxiv). It has

   Definition 4.1. ([6]) An ∞-prestack F has an obstruction theory if (i) F is infinitesimally cohesive (ii) F has a cotangent complex

   So I was interested to see the uptake of Urs’ ’infinitesimal cohesion’, but [6] points to Toen and Vezzosi’s Homotopical Algebraic Geometry II (arxiv). I guess the reference is to their definition 1.4.2.1

   (2) A stack F has an obstruction theory (relative to (C, C0,A)) if it has a (global) cotangent complex and if it is infinitesimally cartesian (relative to (C, C0,A)).

   Is Banerjee suggesting then that infinitesimally cartesian and infinitesimally cohesive are the same? But the latter applies to -toposes not stacks. Strange, n’est-ce pas?

   (EDIT: Oh, I see other people are using it differently, e.g., Lurie in DAG-XIV, Definition 2.1.9. Disambiguation needed?)

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 27th 2013
   • (edited Jun 27th 2013)
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   Author: Urs
   Format: MarkdownItexHi, thanks for pointing this out, I had missed that. I have added a brief entry _[[cohesive infinity-prestack]]_ and disambiguated at _[[cohesive (infinity,1)-topos]]_.

   Hi, thanks for pointing this out, I had missed that.

   I have added a brief entry cohesive infinity-prestack and disambiguated at cohesive (infinity,1)-topos.