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Results tagged with higher-category-theory
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user 5587
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
2
votes
A (too easy) normalization of a lax-funtor between 2-categories ?
It seems to me that your question woud be clearer if you stated more precisely the axioms for lax functors. Anyway, while I am unsure as to what you have in mind, I guess that "lax functors" and "norm …
- 2,413
3
votes
What's an initial object in a poset-enriched category?
Dimitri Ara has just brought this question to my attention. Perhaps you will find the following useful.
Let us say that an object $z$ of a $2$-category $\mathcal{A}$ has a terminal object if, for ev …
- 2,413
9
votes
1
answer
791
views
How do various notions of natural transformation relate to various notions of homotopy in $2...
In what follows, $2$-categories will be strict, and "$2$-functor" will mean "strict $2$-functor". (Please mention which terminological conventions you are using when answering.) I guess that the answe …
- 2,413
11
votes
1
answer
722
views
Is there any elementary text unravelling the definitions of 2-category, lax functor and lax ...
The question is in the title.
My current research subject is the homotopy theory of $2$-categories. It may be slightly unreasonable to expect my PhD thesis to be read or even looked at by people outs …
- 2,413
19
votes
1
answer
874
views
Does the category of strict $2$-categories together with Dwyer-Kan equivalences provide a mo...
The question is the title.
In what follows, all $2$-categories and $2$-functors will be strict. Let $2-Cat$ denote the categories whose objects are $2$-categories and whose morphisms are $2$-functors …
- 2,413
12
votes
0
answers
467
views
What is the history of the notion of subdivision of categories?
A recent answer by Peter May prompts me to ask a question which I have been considering to ask for several months. (The reason why I have not asked it before is that it is not directly related to my r …
- 2,413
16
votes
Conjectures in Grothendieck's "Pursuing stacks"
This is more a comment than an answer, but its length makes me post it as an answer. I want to react to what I have just read, for the first time, about "Pursuing Stacks" at the nLab, and the words us …
- 2,413