Sentence examples for model category and from inspiring English sources

It is elementary to check that (C_cdot (A_cdot )) is a stable model category, and (langle C^{pf}_cdot (A_cdot ),C_cdot (A_cdot ) rangle ) is a stable model pair in the sense of Definition 2.12.

We give an overview of existing enhancement techniques for derived and trianguated categories based on the notion of a stable model category, and show how it can be applied to the problem of gluing triangulated categories.

Since the notions of a model category and a stable model pair are self-dual, Proposition 3.8 immediately implies an analogous statement for left comma-categories and left-derivable functors.

If phonons are treated as particles in a free-gas model category and the phonon dispersion relations were not fully taken into account, there will be an approximately similar decreasing tendency of the LTC versus porosity with that of the ETC for metallic nanoporous materials.

Filters on the initial models' category page include model categories and recently-used models.

In the category model, categories and objects are used to represent different knowledge structures; arrows and pullbacks are used to sketch diverse connection between objects; functors are utilized to reveal the structure-preserving mapping between categories in specification and verification.

While [7] only deals with spaces and spectra, the approach has been generalized to a large class of stable and unstable model categories, and this generalization is now known as "Bousfield localization".

However, completely dispensing with model categories and developing a replacement such as (II) above from scratch would be a huge enterprise, and at present, we are not ready to do it.

The enhancement we suggest is based on stable model categories, and the fact that these produce enhancements has been known since at least [26], and probably goes back to Goodwillie and/or Franke (informally, it was probably known to Quillen, although since the notion of a stable model category is not in [39], his remark in [39, I, §3, Prop. 4] to this effect makes no sense).

Interviews were audio-taped and transcribed for thematic analysis using the Payback Framework and the Logic Model categories and scope notes [ 6].

A series of open-ended questions asked about where the logic model categories and whether the connections between the different categories (e.g. immediate, intermediate, and final outcomes) made sense.